THE ANNALS OF THE COMPUTATION LABORATORY
OF HARVARD UNIVERSITY
VOLUME I
LONDON : GEOFFREY CUMBERLEGE
OXFORD UNIVERSITY PRESS
A MANUAL OF OPERATION
FOR THE
AUTOMATIC SEQUENCE CONTROLLED
CALCULATOR
BY
THE STAFF OF THE COMPUTATION LABORATORY
WITH A FOREWORD BY
JAMES BRYANT CONANT
CAMBRIDGE, MASSACHUSETTS
HARVARD UNIVERSITY PRESS
1946
170S
Copyright, 1946
By the President and Fellows of Harvard College
(Reproduction in whole or in part is authorized and permitted.)
1 ne opinions or assertions contained nerein are tne private ones
of the writers and are not to be construed as official or reflecting
the views of the Navy Department or the naval service at large.
Printed in the United States of America
STAFF OF THE COMPUTATION LABORATORY
Comdr. Howard H. Aiken, USNR
Officer in Charge
Lt. Comdr. Hubert A. Arnold, USNR
Lt. Harry E. Goheen, USNR
Lt. Grace M. Hopper, USNR
Lt(jg) Richard M. Bloch, USNR
Lt(jg) Robert V. D. Campbell, USNR
Lt(jg) Brooks J. Lockhart, USNR
Ens. Ruth A. Brendel, USNR
William A. Porter, CEM
Frank L. Verdonck, Yi/c
Delo A. Calvin, Sp(I)i/c
Hubert M. Livingston, Sp(I)i/c
John F. Mahoney, Sp(I)i/c
Durward R. White, Sp(I)i/c
Geary W. Huntsberger, MMS2/C
John M. Hourihan, MMS3/C
Kenneth C. Hanna
Joseph O. Harrison, Jr.
Robert L. Hawkins
Ruth G. Knowlton
Eunice H. MacMasters
Frederick G. Miller
John W. Roche
Robert E. Wilkins
FOREWORD
No combination of printed words can ever do justice to the real story of an
undertaking in which cooperation between men of capacity and genius is of the
essence. The development of the IBM Automatic Sequence Controlled Calculator
is such a story, with many fascinating chapters. To understand the significance
of this fruitful collaboration between the International Business Machines Cor-
poration and Harvard University one would have to trace the history of this
company, which for many years has been collaborating with leading universities
and research organizations and continuously developing and adapting its equip-
ment for use in the fields of scientific computations. Harvard University's need
for a machine such as the IBM Automatic Sequence Controlled Calculator has
long been a matter of discussion in several of the scientific departments of the
University. Because of the well-known policy of the International Business
Machines Corporation, Professor Aiken of our staff turned to this company to
discuss the possibility of building a calculating machine. To quote from Mr.
Aiken's own words,
"Our first contact with that company was with Mr. J. W. Bryce. Mr. Bryce
for more than thirty years has been an inventor of calculating machine parts, and
when I first met him he had to his credit over four hundred fundamental inventions
— something more than one a month. They involved counters, multiplying and
dividing apparatus, and all of the other machines and parts which I have not the
time to mention, which have become components of the Automatic Sequence
Controlled Calculator. . . .
"With this vast experience in the field of calculating machinery, our suggestion
for a scientific machine was quickly taken and quickly developed. Mr. Bryce at
once recognized the possibilities. He at once fostered and encouraged this project,
and the multiplying and dividing unit included in the machine is designed by him.
"On Mr. Bryce's recommendation, the construction and design of the machine
were placed in the hands of Mr. C. D. Lake, at Endicott, and Mr. Lake called into
the job Mr. Frank E. Hamilton. and Mr. Benjamin M. Durfee, two of his associates.
"The early days of the job consisted largely of conversations — conversations
in which I set forth requirements of the machine for scientific purposes, and in
FOREWORD
which the other gentlemen set forth the properties of the various machines which
they had developed, which they had invented, and based on those conversations
the work proceeded until the final form of the machine came into being." ^
It is not my function in this brief foreword to attempt to summarize the
detailed history of the development of the IBM Automatic Sequence Controlled
Calculator; this has been done admirably in a little booklet published by the
International Business Machines Corporation. The readers of this and subsequent
volumes will, however, be interested in the fact that a whole series of inventions
by IBM engineers are incorporated in the machine as basic units; the names of
Mr, Bryce and Mr. Lake appear frequently on such a list. Here is a striking
example of the way in which the accomplishments of engineers of a great corpora-
tion may enrich many fields of human endeavor. While the public has frequently
been told of the ways in which advances in pure science benefit industry, all too
little is known of the way in which advances in industry benefit science. I hope
the story of the IBM Automatic Sequence Controlled Calculator may to some
degree right the balance.
On August 7, 1944, Mr. Thomas J. Watson, on behalf of the International
Business Machines Corporation, presented Harvard University with the IBM
Automatic Sequence Controlled Calculator. Since that date the machine has been
in constant use by the Navy Department on confidential work. Therefore, Mr.
W T atson's gift came at a time when the new instrument his company had created
was able to serve the country in time of war, before being used for the peaceful
advance of knowledge. It will serve in the future as a focal point for certain types
of mathematical work which the machine is unique in handling. I am told it is
already clear that highly significant discoveries in pure and applied science will
be possible through its use. Therefore, I cannot refrain from concluding this brief
foreword by paying tribute to Mr. Watson. Harvard is indebted to him for a
most generous gilt; tar more important, tne scientific wuim is m^D^a — ^i~
for the development by his company of new tools which he has ever been ready
*~ _,.*. „+ 4-u*> a'ict*™*] rsf tVi*» cripntifir and learned world-
hj uui etc tii^- uiop
/V^Ufc*-*
James Bryant Conant
PREFACE
In May 1944, the Staff of the Computation Project began operations with
the Automatic Sequence Controlled Calculator as an activity of the Bureau of
Ships. One of the first tasks undertaken was the preparation of a report setting
forth the coding procedures of the calculator. This was followed by detailed
plugging instructions, which unfortunately were hardly completed before the code
book was out of date. In the succeeding months, computing techniques were
developed so rapidly that stabilized operating instructions could not be prepared.
At the same time, many mathematicians, physicists, and engineers requested
copies of such data on operating techniques as were available in the laboratory.
This general and widespread interest encouraged the Staff to publish this Manual
of Operation as the first volume of the Annals of the Computation Laboratory,
rather than as a mimeographed compilation of notes as originally intended. Thus
the Manual is unusual in that it is an outgrowth of notes prepared by the Staff
primarily for their own use. The Manual is also exceptional in that it represents
the work of a great many people whose efforts have been closely integrated as is
necessary in the operation of large-scale calculating machines, Chapters I and II
represent extensions and revisions by Lt. Grace Murray Hopper, USNR, of the
writer's old notes, many of which were written before work on the calculator was
begun. Chapter III was written by Lieutenant Hopper with the collaboration of
other members of the Staff. Chapters IV and V represent the outgrowth of the
original code book and plugging instructions prepared by the writer and Lt(jg)
Robert V. D. Campbell, USNR. Nearly every member of the Staff has made con-
tributions to these chapters, but Lt(jg) Richard M. Bloch, USNR, especially
should be mentioned. Chapter VI is made up of the solutions of elementary
examples chosen from those assigned by the Officer in Charge to new members of
the Staff as part of their instruction in the use of the calculator. Those given
in Chapter VI were largely the work of Lt(jg) Brooks J. Lockhart, USNR.
The bibliography of numerical analysis is the result of the library work of
the Staff in connection with the problems assigned to the project. Work on the
bibliography was begun by Lt. Comdr. Hubert A. Arnold, USNR, and completed
by Lt. Harry E. Goheen, USNR, assisted by Ens. Ruth A. Brendel, USNR.
PREFACE
The appendices were prepared by Lieutenant Hopper with the assistance of
Ensign Brendel, Robert L. Hawkins, and Eunice H. MacMasters. Mrs. MacMasters
drew all the figures and diagrams in the book. Ruth G. Knowiton and Frank L.
Verdonck, Yi/c, USNR, are responsible for the typography. The photographs of
the calculator and the films from which the plates for printing the book were
made are the work of Paul Donaldson, photographer of Cruft Laboratory. Lieu-
tenant Hopper also acted as general editor, and more than any other person is
responsible for the completion of the book.
In less than two years, twenty-three reports were completed for the Bureau
of Ships. On the first of January 1946, the project was transferred to the Bureau
of Ordnance under whose cognizance it is now functioning. The gratitude of the
Staff is extended to the Bureau of Ordnance and to the Bureau of Ships for the
privilege of working with the calculator.
This Manual was made necessary by the existence of the calculator itself.
The writer therefore takes this opportunity to express his appreciation to Thomas
J. Watson, President of the International Business Machines Corporation, for his
support during the years the machine was under construction, and to C. D. Lake,
F. E. Hamilton, and B. M. Durfee, engineers of the company, who together with
the writer are the coinventors of the machine.
Howard H. Aiken
Commander,USNR
Officer in Charge
Cambridge Massachusetts
March 1946
CONTENTS
Chapter Page
I Historical Introduction 1
II Description of the Calculator . . . . 10
m Electrical Circuits 53
IV Coding 98
V Plugging Instructions 245
VI Solution of Examples 287
Bibliography 338
Introduction to the Appendices 405
Appendix
I Sequence Codes 411
II Sequence Circuits 431
HI Register Circuits 437
IV Multiply Unit Circuits. . . . 457
V Divide Unit Circuits 499
VI Relay List 528
VTI Cam List. 550
Vm Fuse List 555
Index 557
LIST OF PLATES
Number Facing
Page
I Calculating Wheels designed by Charles Babbage 1
II Front View of the Calculator 6
HI Front View of the Calculator 7
IV Rear View of the Storage Counter Unit and the Multiply-Divide Relay Panel . . 10
V Rear View of the Multiply-Divide Counters and Relay Panel 11
VI Sequence Control Mechanism 14
VH Tape Racks 15
Vm Switches 16
IX Storage Counters 17
X Storage Counter Relays 20
XI Multiply-Divide and Functional Counters 21
XII Sequence Control Mechanism and Interpolators 38
XIII Interpolator 39
XIV Typewriters, Card Feeds and Card Punch 42
XV Tape Punch 43
XVI Relays and Cam 54
XVII Storage Counter 55
I Calculating Wheels designed by Charles Babbage
CHAPTER I
HISTORICAL INTRODUCTION
" If, unwarned by my example, any man shall undertake and shall succeed in really
constructing an engine embodying in itself the whole of the executive department of mathe-
matical analysis upon different principles or by simpler mechanical means, I have no fear
of leaving my reputation in his charge, for he alone will be fully able to appreciate the
nature of my efforts and the value of their results ."
Charles Babbage
"The Life of a Philosopher" (1864)
The desire to economize time and mental effort in arithmetical computation, and to eliminate
human liability to error, is probably as old as the science of arithmetic itself. This desire has led to
the design and construction of a variety of aids to computation beginning with "groups of small objects
such as pebbles, used first loosely, later as ' counters ' on ruled boards, and later still as beads
mounted on wires fixed in a frame, constituting the abacus".
It seems most likely that the abacus originated in the Tigris -Euphrates valley, and that its use
traveled both east and west along the routes of the caravans. Elaboration of the instrument and later
development of the techniques of its manipulation made it applicable to multiplication, division, and
even to the extraction of square and cube roots, as well as to addition and subtraction for which the
instrument was probably originally intended. Indeed, the abacus, despite its ancient origin, is still
in use by the oriental peoples. This long period of utility is due not only to the simplicity of the instru-
ment, but also due to two fundamental notions inherent in its construction. Place significance, or the
use of zero to signify an empty column, is provided by the several wires on which the beads are strung.
Moreover, the principle of carry, whereby the (n + l)st column is increased by one when the nth has
become exhausted, is applied in adding.
After the invention of the abacus, five thousand years elapsed before the next computational aid
was developed. During this time, gears and pointers were used in the design of clocks. These machine
elements, and more especially a wheel which at the end of a complete revolution gave impetus to a
second wheel, paved the way for the development of calculating machinery.
In 1617, John Napier, following his invention of logarithms, published an account of his number-
's
ing rods, known as " Napier's bones". Various forms of the bones appeared, some approaching the
HISTORICAL INTRODUCTION
, . . - ... . ..., ..... „ ....,..,....„..,...., . , ,.,._._ . , ,_4
Deginnmg 01 mecnamcai computation. ouDsequem. io me miroaueuun 01 lugariuims, uia suae ruie
was developed by Oughtred (1630), Everard (1755), Mannheim (1858) and others. The slide rule re-
ceived wide recognition from scientists as early as 1700. Particularly in engineering design, the slide
rule has proved an invaluable instrument. It has been increasingly applied to the solution of problems
requiring an accuracy of not more than three or four significant figures and where the total bulk of
the computation is not extensive. The slide rule is probably the most useful computational aid so far
devised; its low cost, ease of construction, and the simplicity of its principle of operation and of its
use, make the instrument of primary importance. The slide rule is probably the ancestor of all those
calculating devices whose operation is based upon an analogy between numbers and physical magni-
tudes- in which the commuted results are obtained b" ohvsical measurements s Manv such snalosn. 7
devices have since been constructed. Examples of these are the planimeter, integraph, Kelvin's tide
predicter and finally the differential analyzer. All analogy devices, like the slide rule, are limited to
the accuracy of a physical measurement.
5
It was Blaise Pascal who, in 1642, designed and built the first mechanical adding machine in
the modern sense of the term. Incidentally, it should be noted that Pascal's machine was designed not
to further scientific research but rather for use in his father's mercantile business. Itwas an account-
ing machine and as such was the forerunner of the modern accounting machine and cash register. The
design of Pascal's machine depended upon rotating wheels and provided for carry by mechanically
turning the wheel of next higher order one position when the lower passed from nine to zero. The
direct actuation of a numbered wheel and the secondary feature of effecting carry (which seem to have
been first used in an adding machine by Pascal) are the foundation on which nearly all mechanical cal-
culating machines have since been constructed.
Naturally, any machine designed for addition may also perform subtraction by means of comple-
mentary numbers. The complement on ten of a number is that second number which must be added to
the first in order to obtain a power of ten. The complement on ten of a number may be read off from
left to right by taking the complement on nine of each successive digit except the last on the right, of
which the complement on ten must be taken. Thus the complement on ten of 7528 is 2472. If it is de-
sired to subtract 7528 from any number, for example, 38421, the work may be written,
HISTORICAL INTRODUCTION
38421 - 7528 = (38421 - 10000) + (10000 - 7528) = 28421 + 2472 = 30893.
This procedure may further be simplified by the use of complements on nine and "end around carry" .
End around carry implies carry from the highest column of a machine to the lowest column of the
machine. The complement on nine of 7528 in a six column machine is 992471. Subtraction now becomes
038421 + 992471 + 000001 = 030893,
where the third term, 000001, is supplied by end around carry.
If any number, 007364, is added to 999999, operation of the machine will yield,
999999 + 007364 + 000001 - 007364,
where the third term is again the result of end around carry. Since, under these conditions, 999999 is
a number having the properties of zero for machine purposes, the complement on nine of any number
may be adopted as the negative of the number. Clearly, an n digit calculating machine must be sup-
plied with (n + 1) columns, the highest being reserved for the algebraic sign, zero and nine being
positive and negative respectively.
The next major development in mechanical aids to numerical computation came in 1666 when
7
Samuel Morland built a machine similar to Pascal's, adapted to multiplication by repeated addition.
Q
Independently, in 1671, Leibnitz conceived a multiplying machine and finished it in 1694. In Pascal's
machine the wheels were set and turned individually by hand; in Leibnitz' machine all wheels were
set and turned simultaneously by a crank to a previously determined position. In the "stepped reckoner",
Leibnitz added a device which still occurs as a component part of modern calculating machines.
In the years that followed, methods of carrying were refined and calculating machines soon added
by a process not used by the human mind. The addition of two numbers, 3279 and 8935, requires the
following mental steps:
3279
8935
4 add units digits
1 carry
I? add tens digits
1 carry
214 add thousands digits
1 carry
2214 add ten-thousands digits
1 carry
T52T?
HISTORICAL INTRODUCTION
In adding two numbers, a machine may add all digits simultaneously, store the inuiviuuaj. carry num-
bers and then perform all carrying operations simultaneously. For example,
3279
8935
1104 sum without carry
1111 carry numbers
T22I4"
Thus the machine consumes not more than two steps for any addition, no matter how many significant
digits there may be in the terms of the addition.
From the seventeenth century on, it was even more evident that precise and rapid methods of
computation were required. The computation of tables of logarithms demanded by Napier's discovery,
of tables of sines and cosines- of tables of tides needed bv faster and more extensive navigation and
of the astronomical tables envisioned by Kepler, accentuated this need. Among many others, Gauss,
9
Cayley , Tchebychev, Maxwell and Kelvin all attempted to devise or improve computational aids . Natu-
rally these men all considered mechanical calculation largely from their own point of view, the desire
to further scientific advancement. Despite this widespread interest, the development of modern cal-
culating machinery proceeded slowly until the growth of commercial enterprise and the increasing
complexity of accounting made mechanical computation an economic necessity . Thus the ideas of the
physicists and mathematicians, who foresaw the possibilities and gave the fundamentals, were turned
to excellent purposes, but differing greatly from those for which they were originally intended.
It was not until just before the beginning of the nineteenth century that any attempt was made to
build highly specialized calculating machines designed for the mathematical and physical sciences. A
Hessian military engineer, J. H. Miiller, seems to have had the first idea of a difference engine in
1786. But this idea remained in a purely theoretical state and was without doubt forgotten when, in
1812, it occurred to Charles Babbage and he set about the actual construction of such an engine.
This engine was to "perform the whole ope ration -(the computation and printing of tables of functions)
..12
-without any mental attention when once the given numbers have been put into the machine"." A first
model was built in 1820-22 and consisted of six columns using second differences. In 1823, the con-
struction of an engine using twenty-six significant digits and sixth differences was begun with the aid
of a subvention from the British government. The construction continued until 1833 when the govern-
HISTORICAL INTRODUCTION
ment aid was withdrawn. The unfinished machine is preserved in the collections of the Science
Museum in South Kensington. It should be borne in mind that the difference engine, although a highly
useful scientific instrument, was still a specialized machine being intended for the sole purpose of
tabulating the values of a function for equidistant values of the argument.
Having been unable to complete the difference engine, Babbage embarked upon the creation of a
1 ^
far more ambitious concept, an " analytical engine ". Though the terms of the problem proposed
were enough to stagger the contemporary imagination, he attempted to design a machine capable of
carrying out not just a single arithmetical operation, but whole series of such operations without the
intervention of an operator. The numbers in the first part of the machine, called the "store", were to
be operated upon by the second part of the machine, called the "mill". A succession of selected oper-
ations were to be executed mechanically at the command of a "sequence mechanism" (a term unknown
to Babbage). For this latter, he intended to use a variation of the Jacquard cards. 14
15
These cards, the precursors of Hollerith^ punched cards, were used by the Jacquard weavers
to control the looms to produce and reproduce the patterns designed by the artists. The designs were
first sketched as they were to appear in the finished product, transferred to squared paper and used
as guides for punching the cards. The cards allowed certain needles to be extended through the punched
holes, thereby controlling hooks which, in turn, raised particular warp threads to produce the desired
pattern. In order to continue the weaving of the same design, the cards were interlaced with twine in
an endless sequence so that one card was brought into position immediately after another was used.
Holes were punched for the lacings as well as for the pegs which guided the cards over a cylinder.
In adapting these cards for use in his machine, Babbage required two decks: one of variable
cards and one of operational cards. The first set was designed to select the particular numbers to be
operated upon from the store; the second set, to select the operation to be performed by the mill. The
deck of operation cards therefore represented the solution of a mathematical situation independent of
the values of the parameters and variables involved. Thus the analytical engine was to have been
completely general as regards algebraic operations.
In order to use selected values of transcendental and other functions, the engine was to be equip-
ped with a mechanism to call for such functions. Having stopped and rung a bell, a certain part of the
HISTORICAL INTRODUCTION
machine would indicate that a particular value of a particular function was required. The attendant
would then insert a punched card containing the desired function and its argument. The machine then
checked the card to make sure that it was the one requested, by subtracting the argument of the in-
serted card from the argument standing in the machine. If the difference was zero, the engine would
continue its computation. If an incorrect card was supplied, the engine would "ring a louder bell and
stop". 16
As in the difference engines, the analytical engine was to print its own results. Further, a
mechanism was to have been added for punching numerical results in blank cards for future use. In
this way, the engine could compute the tables required and punch its own cards " entirely free from
_ _ ,: 17
error .
In 1852 Charles Babbage said: "At a period when the progress of physical science is obstruct-
ed by that exhausting intellectual and mental labor indispensable for its advancement, which it is the
object of the Analytical Engine to relieve^ think the application of machinery in aid of the most com-
plicated and abstruse calculations can no longer be deemed unworthy of the attention of the country.
In fact there is no reason why mental as well as bodily labor should not be economized by the aid of
machinery". 18 He felt most strongly that the time must arrive when no table would ever be calculated
or printed except by machine. It was of the utmost importance, he thought, to accelerate the arrival
of the time, "when the completion of a calculating engine shall have produced a substitute for -(manual
computation, so that) -the attention of the analysts will naturally be directed to simplifying its appli-
1Q
cation by a new discussion of the methods of converting analytical formulae into numbers" .*"
In 1834, George Scheutz, 20 a printer in Stockholm, built a less ambitious difference engine with
the aid of a grant from the Swedish government. The machine was completed in 1853 and used for the
computation and printing of tables of logarithms, sines and logarithms of sines. It was exhibited at
the Paris exposition in 1855 and later became the property of the Dudley Observatory in Albany, New
York. From Sweden also came Wiberg's difference machine 21 (1863) which was presented to the
Academy of Sciences in Paris by the astronomer Delaunay.
One of the first Americans to build a difference machine was G.B.Grant of Cambridge, Massa-
22
chusetts, who needed a machine for his " computing for excavation and embankment " . Encouraged
II Front View of the Calculator
HI Front View of the Calculator
HISTORICAL INTRODUCTION
in his designs by Professor Wolcott Gibbs of the Harvard Mining School, Grant successfully built a
small model in 1871 under Professor Benjamin Peirce,then superintendent of the Coast Survey. This
machine was designed to contain the usual calculating and printing parts contained in Babbage's and
Scheutz' engines, but with considerable improvement in the printing mechanism. 23 Grant's indebted-
ness for assistance in his study was expressed to John N. Bachelder of Cambridge and to Professors
Eustis, Winlock, and Whitney of Harvard.
In 1893, Torres restated Babbage's problem: to construct a purely automatic calculator capa-
ble of carrying out any succession of arithmetical operations on any given numbers, without human
intervention from the time when the operations have been indicated until the time when the machine
sends the results to a printing device. Torres had available electro-mechanical counters and both
electrical and mechanical controls. He gave a solution to the problem and proved that such a machine
was theoretically possible, although his solution was not free from certain complications due to the
multiplicity of the electrical connections assumed.
Despite the partial successes of Scheutz, Wiberg and Grant, the problem of designing calculating
machinery was abandoned by the students of science and left in the hands of the inventors. For the
purposes of accounting, these men, both in this country and abroad, with the aid of the improved ma-
terials and tools created during the industrial revolution, succeeded in bringing key driven calculating
machines to a high state of perfection. The use of punched cards as a means of storing numbers and
all the associated mechanisms, developed by Bryce, Carrol, Lake, Hamilton, Daly and Durfee of the
International Business Machines Corporation brought the possibility of scientific calculating machinery
again into a position where the situation could be viewed with some hope of success.
In 1906,H.P.Babbage,son of the philosopher, completed a part of the analytical engine. A table
of multiples of -r which it computed to twenty-nine significant digits was published as a specimen of
25
its work. Clearly then, Babbage's failure to complete either of his projects himself was not due to
a lack of understanding of the principles and purposes of the engines that he designed, but rather to
his lack of machine tools, materials of construction and electrical circuits. Of these deficiencies, the
first was probably the most important. Also, Babbage was a "natural philosopher". 26 His machines
were perforce built by hired engineers. 27 He himself was not " well -acquainted " with the medium in
HISTORICAL INTRODUCTION
wmcn ne uiiuse iu wui&, mciciuic, uiuugii mo jji mbi|».vu ty^av. M .*,v,.. ~„«.«.~ — ,, ~ D
was successful to a limited extent, it remained for the twentieth century and the evolution of advanced
mechanical and electrical engineering to bring his ideas into being.
References
1. D. Baxandall, Catalogue of the Collections in the Science Museum, South Kensington. Mathe-
matics I Calculating Machines and Instruments (1926), p. 7.
2. F. Cajori, History of Mathematics (1919), p. 7; L. Jacob, Le calcul mecanique (1911), p. 3; C.G.
Knott, The calculating machine of the east: the abacus, in Modern Instruments and Methods of
Calculation, E. M. Horsburgh, ed. (1914), pp. 136-154; M. d'Ocagne, Le calcul simplifie (1905),
p. 7.
3. G. A. Gibson Na n ier and the invention of logarithms, in Modern Instruments and Methods of
f!al<f*-'ilatinn. H. M. Horsbursh. ed. (1914). dd. 1-16.
4. F. Cajori, History of the Logarithmic Slide Rule (1909); F. Cajori, William Oughtred (1916); A.
Galle, Mathematische Instrumente (1912), pp. 1-21; Jacob, op. cit., pp. 96-109; d'Ocagne, ibid.,
pp. 105-128; G. D.C.Stokes, The slide rule, in Modern Instruments and Methods of Calculation,
E.M. Horsburgh, ed. (1914), pp. 155-180.
5. S. Chapman, Blaise Pascal (1623-1662), Nature, 150; 508-509 (1942); d'Ocagne, ibid., pp. 24-
31; J. A. V. Turck, Origin of Modern Calculating Machines (1921), pp. 11-13.
6. Crompton Patent, U. S., No. 1514954, claim no. 7.
7. Baxandall, op. cit., pp. 8, 14-16; d'Ocagne, ibid., p. 30.
8. Jacob, op. cit., pp. 39-46; d'Ocagne, ibid., p. 30; M. d'Ocagne, Machines a calculer (1922),
pp. 21-23.
9. Baxandall, op. cit.; Jacob, op. cit.; d'Ocagne, ibid.; Modern Instruments and Methods of Calcu-
lation, E. M. Horsburgh, ed. (1914).
10. F. Cajori, History of Mathematics (1919), p. 485; Jacob, op. cit., pp. 114-115; d'Ocagne, Le
calcul simplifie" (1905), p. 82.
11. Charles Babbage, Passages from the Life of a Philosopher (1864), chap. V, "Difference Engine
No. I", pp. 41-96; Baxandall. op. cit., pp. 30-34.
12 . Babbage , ibid ., p . 41 .
13. Babbage, ibid., chap. VIE, "Of the Analytical Engine" , pp. 112-141; Jacob, op. cit., pp. 188-190;
P. E. Ludgate, Automatic calculating machines, in Modern Instruments and Methods of Calcu-
lation, E.M. Horsburgh, ed. (1914) pp. 124-127.
14. Babbage, ibid., pp. 116-117.
15. E. A. Posselt, The Jacquard Machine (189-?), pp. 9. 17-20, 85-102.
16. Babbage, ibid., pp. 119-120.
HISTORICAL INTRODUCTION
17. Babbage, ibid., p. 122.
18. Babbage, ibid., p. 106.
19. Charles Babbage, Economy of Machinery and Manufactures (1846), p. 195.
20. Charles Babbage, Passages from the Life of a Philosopher (1864), p. 48; Baxandall, op. cit.,
pp. 32, 34-36; Jacob, op. cit., pp. 115-117; d'Ocagne, ibid., pp. 83-86.
21. Jacob, op. cit., pp. 117-123; d'Ocagne, ibid., pp. 86-87.
22. G. B. Grant, On a new difference engine, American Journal of Sciences and Arts (3) 2; 113-117
(1871).
23. Jacob, op. cit., p. 45.
24. Jacob, op. cit., pp. 165-169, 189-200; d'Ocagne, ibid., p. 95; M. d'Ocagne, Machines a calculer
(1922), pp. 49-53.
25. Ludgate, op. cit., p. 127.
26. Cf. the title of his book, "Passages from the Life of a Philosopher".
27. Babbage, ibid., pp. 79-82.
28. Babbage, ibid., p. 92.
10
CHAPTER II
DESCRIPTION OF THE CALCULATOR
"Interpolation ist die Kunst zwischen den Zeilen einer Tafel zu lesen."
T.N. Thiele
"Interpolationsrechnung". (1909)
Although a method of interpolation bearing some resemblance to modern central difference
1 2
formulae was used by Briggs in 1624, it was not until 1670 that James Gregory introduced the notion
of interpolation based upon the representation of functions by means of approximating polynomials.
The use of approximating polynomials reduced the whole problem of the tabulation and subtabulation
of functions, over a limited range of the argument, to the arithmetical operations of addition and sub-
traction alone, once the necessary initial differences were established. Thereby the basic principle
was given for the operation of the difference engines briefly mentioned in the foregoing chapter.
Further development of the theory of interpolation by Newton, Stirling and others laid the foun-
dation for the Calculus of Finite Differences set forth as a new branch of mathematics by Taylor in
1715". Since that time the subject has been increasingly developed so that now a variety ol techniques
are available for numerical differentiation and for the numerical evaluation of definite integrals . The
latter include the formulae of Gregory, Cotes, Euler-Maclaurin, Simpson, Weddle, Gauss, Tchebychev
4
and Steffensen .
In 1883, Adams and Bashforth , using the methods of finite differences, devised a technique for
the numerical solution of ordinary differential equations . This has been followed by many other methods ,
R 7
that given by Runge in 1895 , and improved and extended by Kutta in 1901 being, perhaps, the best
known. More recently methods have been given for the numerical solution of partial differential
equations. The extension and application of these methods present one of the most important prob-
lems in mathematics at the present time.
In every case, the effect of the numerical methods has been to reduce the processes of mathe-
matical analysis to a sequence of the five fundamental operations of arithmetic: addition, subtraction,
multiplication, division and reference to tables of previously computed results. Thus the calculus of
finite differences has become the bridge between mathematical analysis and numerical computation.
IV Rear View of the Storage Counter Unit and the Multiply- Divide Relay Panel
V Rear View of the Multiply -Divide Counters and Relay Panel
11
DESCRIPTION OF THE CALCULATOR
Unfortunately, the application of numerical methods is attended by a relatively great amount of compu-
tational labor, so that while existing types of calculating machinery are sufficient from a theoretical
viewpoint, they are entirely inadequate from a practical standpoint. It is for this reason that the
Automatic Sequence Controlled Calculator has been constructed.
In 1937, the calculator was visualized " as a switchboard on which are mounted various pieces
of calculating machine apparatus. Each panel of the switchboard is given over to definite mathematical
8
operations." It stands today much as originally imagined, in a stainless steel and glass case, fifty-
one feet long and eight feet high, (Plates n and III). Two panels, each six feet long, extend at right
angles from the back of the machine. Between these two panels is the four horsepower motor which
drives the mechanical parts, (Plates IV and V). Altogether the machine weighs about five tons.
The calculator is equipped with a central multiplying and dividing unit together with seventy-two
adding- storage registers and sixty constant registers corresponding to the mill and store of Babbage's
proposed analytical engine. In addition, the machine is supplied with electro-mechanical tables of
log x, lCr and sine x. Three non-linear interpolator units are capable of interpolation of any order
up to and including the eleventh, on functions supplied to them in the form of perforated paper tape.
Other computing elements included are: two card feeds for supplying the machine with empirical or
other data, a card punch for punching results in tabulating machine cards, two automatic typewriters
for recording computed results and an automatic sequence unit having control of the machine as a whole.
The sequence control unit, shown in Plate VI, consists of a main drive sprocket drum over which
runs a perforated paper tape, called a control tape, together with such gears, cams and clutches as
are necessary to advance the drum and tape one line of perforations at a time. The tape is strung on
racks in back of the machine as shown in Plate VII and held taut by a roller just below the sequence
mechanism. The sequence unit is equipped with a set of twenty-four sensing pins, controlled by a
crosshead, which are advanced at the end of each forward step of the tape to detect the distribution of
holes in one line of the tape and to close electric contacts in the same distribution.
Each horizontal line of the tape has space for twenty-four equidistant holes, these being con-
sidered as three groups of eight holes each, known as the A, B and C groups, (Plate VI). The A group
of holes controls the " out-relays " by means of which all units in the machine are connected to the
12
DESCRIPTION OF THE CALCULATOR
central distribution buss over which numbers are transferred from one unit to another with the aiu Oi
timed electrical impulses later to be described. The B group of holes controls the "in-relays" of all
of the units in the machine. These also connect the units to the central distribution buss, and when
closed, permit the egress of numbers from the buss into the units. Finally, the C group of holes repre-
sent, in general, an operation to be performed on the number in unit A in connection with the number
in unit B.
Each horizontal line of holes perforated in the tape is the equivalent of a single spoken command,
"Take the number out of unit A; deliver it to unit B; start operation C." Since the A, B and C groups
of perforations each contain eight holes, the maximum number of out, in or miscellaneous operational
rslavs which ".sp. he controlled bv the machine is 2 = 256 each. The maximum oossible number of
commands which can be represented by a single line of holes is 2 = (256)° = 16,777,216. Actually,
many of these are not used, and many others are invalid because of special features to be made clear
in Chapter IV on Coding. The number of combinations of coded perforations in use at present is con-
siderably smaller than the maximum possible number. In any event, a very great many possibilities
are available in each line of perforations. Since the number of consecutive lines of holes is in no way
limited, it is apparent that control tapes may be provided with great generality. The reiteration of
the single command, "Take the number out of unit A; deliver it to unit B; start operation C", permuting
A and B over the various units of the machine, while changing the nature of the operation C, is suf-
ficient to guide the machine through any problem of mathematics capable of reduction to the five
fundamental operations of numerical analysis.
At the left of the machine, as well as at the left of Fig. l,are the sixty constant registers. Each
constant register consists of twenty-four manually set ten-pole dial switches designed to accommodate
twenty-three digits and the algebraic sign. Because of their composition, the constant registers are
commonly known as the sixty "switches". Each constant register or switch is connected to the buss
through its out-relay, (Plate VTII), and each is connected to the common transfer terminal of the storage
register invert relay. The normally closed and normally open contacts of this relay are in turn con-
nected to the direct and invert cam controlled contacts, respectively, which furnish the timed electrical
impulses necessary to the transfer of numbers via the buss.
13
FROM FIG. 12
SWITCH
OUT
RELAY
t— .
t— ■
CO
co
CO
L- o-
t— .
DESCRIPTION OF THE CALCULATOR
BUSS
TO FIG. 2
NO. I
NO. 2
NO. 3
SWITCHES
NO. 60
DIRECT / _ 1 _ |
READ- OUT U T
CAM ^-^
CONTACTS
</u
CO
CO
3
GO
STORAGE
COUNTER
OUT- RELAY
STORAGE
COUNTER q—X
INVERT
RELAY
STORAGE
COUNTER
IN-RELAY
NO. I
t_* ..
NO. 2
NO. 3
STORAGE
COUNTERS
t-^-
t—^.
K INVERTED
J READ- OUT
CAM
CONTACTS
50 VOLT
NO. 72
CO
CO
I — ^
CD
TO FIG. 2
D.C.
Figure 1
14
DESCRIPTION OF THE CALCULATOR
To the right of the switches, Fig. I, are shown diagrammaticaliy the seventy-two storage regis-
ters. Each storage register consists of twenty -four electro-mechanical counter wheels. The storage
registers, usually referred to as "storage counters" or more briefly as "counters", have electrical
connections similar to those of the switches. In addition, each storage counter is provided with an in-
relay connected to the buss, a complete set of carry controls and a connection to the negative terminal
of the generator.
Plate IX shows a close-up view of twelve columns of the storage counters 16 and 17 as seen from
the front of the calculator while Plate X shows the relays associated with storage counters in general
and mounted at the back of the machine .
counters 1, 2, 3, ..., 71, 72 are 1, 2, 21, ..., 7321, 74 respectively, while the code numbers of switches
1, 2, 3, ...,59, 60 are 741, 742, 7421, ..., 821, 83 respectively. Similarly, all operations in the cal-
culator have assigned code numbers. For example, code 32 in the operational or miscellaneous group
C controls the storage counter invert relay, and hence is the mathematical equivalent of a minus sign.
A complete discussion of all codes will be found in Chapter IV on Coding; the few here given will suf-
fice for present purposes.
Now let it be required that the number x in storage counter number 3, code 21, be added to the
number y in storage counter number 71, code 7321. This operation may be written,
Take x from ctr. 3 and add it into ctr. 71.
On the other hand, if it is required to subtract x from y , the coding will be written,
OUT
IN
MISC.
21
7321
OUT
IN
MISC.
21
7321
32
Take x from ctr. 3 and by means of the invert relay add
its complement on nine to ctr. 71; i.e., subtract x now
in ctr. 3 from y in ctr. 71.
Returning to Fig. 1, the perforations in the control tape corresponding to code 21 in the Out
column, as interpreted by the sequence mechanism, cause the closure of the out- relay of counter 3,
while the code 7321 in the In column causes the closure of the in-relay of counter 71, The blank in
the Miscellaneous column of the coding is interpreted as a plus sign leaving the storage counter invert
VI Sequence Control Mechanism
VII Tape Racks
15
DESCRIPTION OF THE CALCULATOR
relay in its normally closed position. Thus a complete electrical circuit exists beginning at the posi-
tive terminal of the generator, passing through the cam contacts; through the normally closed contacts
of the storage counter invert relay into counter 3; through counter 3 and its out- relay to the buss; from
the buss to counter 71 through its in-relay; through counter 71 and finally back to the negative termi-
nal of the generator. Hence, the timed electrical impulses produced by the cam contacts are enabled
to transfer the quantity in counter 3 to counter 71 and bring about addition. The detailed mechanisms
by which this is accomplished will be described in Chapter IH.
When it is required to subtract x from y , the whole operation is the same except that code 32
in the Miscellaneous column causes the storage counter invert relay to transfer its contacts. This
causes the complement on nine of x to be read out into the buss instead of x itself. Since all storage
counters are equipped with complete carry controls, including end around carry, addition of the comple-
ment on nine completes the process of subtraction as demanded in the example .
Before further considering the functions of the storage counters, it is necessary to discuss
briefly the means by which the calculator is kept in continuous operation. Most mechanisms, once
started, remain in operation until signalled to stop. By contrast, the calculator continues in operation
only so long as the command "continue operation" is repeated, cycle by cycle, and immediately stops
on the first occasion on which this command fails of being given. A 7 in the Miscellaneous column of
a line of coding instructs the sequence mechanism to continue operation; i.e., to read the next line,
act upon it and step to the line beyond. Every line of coding must contain a 7 in the Miscellaneous
column or its equivalent in the form of some other automatic continue operation code. Since the storage
counter codes are not such "automatic codes", the two examples of coding already cited should read,
Take x from ctr. 3 and add it to y in ctr. 71.
Take x from ctr. 3 and subtract it from y in ctr. 71.
From what has so far been said it should now be clear that the storage counters serve more than
one purpose. Each is a complete adding and subtracting machine, and functions as a storage or memory
OUT
IN
MISC.
21
7321
7
21
7321
732
device, thereby providing the calculator with brackets, parentheses and other signs of association as
16
DESCRIPTION OF THE CALCULATOR
required in matnematicai expressions, in aacuuon, reuiys a»»uui<u.«na wim c»wi ^m*..*.* ^
functions not indicated in the single line diagram, Fig. 1, for reasons of clarity. The nature of these
electrical controls will be set forth in Chapter III; however, their mathematical significance may be
given here.
The quantity in each storage counter may be read out as either a positive or negative absolute
value under the control of the operational codes 2 and 1, respectively, in the Miscellaneous column of
the line of coding. For example, if x lies in storage counter number 23, code 5321, and y in counter
number 34, code 62, then |x| + y may be obtained in counter number 34 by the line of coding,
OUT
IN
MISC. |
j
i
5321
62
72 1
i
Add ! x' to Tr .
The use of absolute magnitudes provides the calculator with a means of dealing with discontinuous
functions. For example,
(x+ !x|)/2x = or 1,
according as x is negative or positive.
Each storage counter may be reset to zero by reading into the counter the complement on ten of
the quantity standing in the counter while the carry controls are disabled. This is accomplished for
any storage counter whose code is A, by the line of coding,
OUT
IN
MISC.
A
A
7
Reset ctr. A.
Inasmuch as a blank other than 7 in the Miscellaneous column of coding has been defined as a plus
sign, the reset coding requires further explanation. The resetting operation is one which occurs with
great frequency. To eliminate the necessity of writing and rewriting a special reset code in the Miscel-
laneous column, special wiring is included in the machine such that the duplication of a storage counter
code in both the Out and In columns of a line of coding resets the counter concerned.
Of all the computing elements in the calculator, the storage counters are the simplest. There-
fore it is relatively easy to alter and to add to their electrical circuits in such a way as not to interfere
with their normal functioning, but at the same time introduce added possible operations. A number of
such special operations have been required in the past, and have been permanently built into the machine .
Vrn Switches
DC Storage Counters
17
DESCRIPTION OF THE CALCULATOR
Counter 70 has been equipped with relay circuits which prefix the algebraic sign of the quantity
in counter 70 to the positive absolute value of the quantity standing in any other storage counter when
the latter is read out under the code 432 in the Miscellaneous column. This feature is especially
valuable when dealing with the interpolation of odd functions, since it is only necessary to evaluate
f(x) in order to have available f(-x) = - f(x) . Counter 70 is usually called the choice counter for
reasons which are not immediately obvious. For instance, the choice counter makes it possible to
use the two identities,
arc tan |x| = x/2 - arc tan l/|x|,
arc tan (-x) = - arc tan x ,
to reduce the labor of computing f(x) = arc tan x, - oo < x < + oo . If |x| - 1 is read into counter 70,
and (l/|x| + |x|)/2 and (l/|x| - |x|)/2 are stored in counters B and C respectively, the addition of C
to B under control of counter 70 will give in counter B,
z=(l/|x| + |x|)/2- (l/|x| - |x|)/2 =|x|, if [x|< 1;
z =(l/|x| + |x|)/2 + (l/|x| - |x|)/2 =l/|x|, if |x| >1.
Thus only arc tan z, £ z £ 1, need be computed by the machine and stored in counter D. If x/4 and
7T/4 - arc tan z are stored in counters E and F respectively, the addition of F to E under control of
the choice counter gives in counter E,
u = t/4 - arc tan z - t/4 = - arc tan z
= - arctan |x|, if ) X | £ 1;
u = "f /4 - arc tan z + "x/4 = ir/2 - arc tan z
= T/2 - arctan l/|x|, if |x| > 1.
Transferring u to counter G under control of the choice counter gives
v = arctan |x|, if | X | £ 1;
v = "Jr/2 - arctan 1/ |x| = arctan [x|, if |x| > 1.
It now remains only to prefix the algebraic sign of x; the choice counter is therefore reset and x read
in. The read-out of v to counter H under control of the choice counter completes the evaluation of f(x),
f(x) = arctan x = arc tan |x|, x >+ 0;
f(x) = arctan x = - arctan |x|, x £ - 0.
18
DESCRIPTION OF THE CALCULATOR
OUT
IN
MISC.
A
732
72
741
732
732
C
B
7432
Inasmuch as the manipulation of the choice counter in the computation of are tan x is typical of
many similar applications, the necessary coding will be given in detail.
Let counter A =x, counter B = (l/|xj + |x|)/2, counter C = (l/|x| - |x|)/2,
switch 1=1, switch 2 = t/4
and counters D, E, F, G, H and 70 be reset and available for computation^
|xj to ctr. 70
- 1 to ctr. 70
ctr. C to ctr. B under control of ctr. 70; ctr. B = z
- _ __^_. s i_i__ ,.±^ «««foT, n or,H Hoiiv^rs it to counter D.
x/4 to ctr. E
X/4 to ctr. F
- arc tan z to ctr. E
ctr. F to ctr. E under control of ctr. 70; ctr. E = u
ctr. E to ctr, G under control of ctr. 70; ctr. G = v
reset ctr. 70
xto ctr. 70
arc tan x to ctr. H
The use of the choice counter to construct discontinuous functions and to choose among two or
more functions is treated in detail in Chapter IV.
Associated with counter 71, the " multiple in-out " counter, are a special set of carry controls
which make a twelve column storage register out of the twelve high order columns of the counter. This
twelve column counter is complete with end around carry, can be independently reset and does not in
anyway interfere with thenormal twenty -four column functioning of counter 71. As shown in Fig. 2, the
multiple in-out counter has extra in- and out-relays which connect the upper twelve columns of the
counterto eitherthe upper orthe lower twelve columns of the buss. Mathematically, this is the equiva-
lent of multiplying by 1 or 10 12 when numbers are read into the counter and by 1 or 10" 12 when
742
E
7
742
F
7
D
E
732
F
E
7432
E
G
7432
732
732
7
A
732
7
G
H
7432
DESCRIPTION OF THE CALCULATOR
19
FROM FIG. I
BUSS COLS. 1-12
n
TO FIG. 3
BUSS COLS. 13-24
FROM FIG.
OUT
RELAYS
IN
RELAYS 9
I
COLS. 13-24
i u
IZL
'-] "- COLS. 1-12
MULTIPLE -IN- OUT COUNTER
(COUNTER 71)
DIRECT Cl
READ- OUT
CAM
CONTACTS
STORAGE
COUNTER
INVERT
RELAY
i3
INVERTED
READ-OUT
CAM
CONTACTS
TO FIG. 3 1 "
50 VOLT D.C.
Figure 2
numbers are read out of the counter depending upon the operational codes employed. (See Chapter IV,
Coding, Multiple In-Out Counter.) In all problems requiring less than twelve significant digits for
computation, the transfer of numbers through counter 71 permits the storage of two quantities in each
of the seventy-two storage counters, thus doubling the storage capacity of the machine. The function
of the multiple in- out counter is most valuable in statistical computation where the quantities dealt
with are large in number and of low accuracy.
20
DESCRIPTION OF THE CALCULATOR
- . . L % ..u!..i. •_ jl jl j t-i~„ 4.%.^ „+~~«-.~^ nnnnoi-l-iT r»f 4-ha /iol *»nl !i+r»r» at th© PTTnPTlSe
JUSI aS Xne mUlllpie Xn-OUL CUUIlLtJl" UUUUICa tlio 01vs.1a.5c \,a.jL*cn_*tjf w u«- v,«.*~-*«*w ~v —.~ -— r
of accuracy, so do the " ganged counters ", 68 and 69, double the accuracy of the machine at the ex-
pense of storage capacity. Counters 68 and 69 are equipped with special carry controls such that they
function as a single storage register consisting of forty-six columns and the algebraic sign which is
repeated in the two component counters. Since this feature has been proved to be of considerable value
in high accuracy computation, counters 64 and 65 have likewise been ganged together. Needless to say,
the inclusion of the special carry controls on counters 64, 65, 68 and 69 do not interfere with their nor-
mal functions. Two lines of coding are required to make a single forty -six column addition, since the
two parts of the number must be added successively. An 8 prefixed to the ordinary read-in codes of
4.u~ jya^g.^ s» ni intipr<; n jpks un the soecial carry controls, The addition of A + B, a forty-six column
quantity lying in counters 35, 34, codes 621, 62, to C + D, standing in counters 69, 68, codes 731, 73,
is coded as :
Add A + B to C + D with special carry controls.
The most important of the specialized storage registers is the automatic check counter, 72.
Mathematically all checks may be reduced to determining that a given quantity c is less in absolute
magnitude than a selected positive tolerance, t; i.e., that t - |c| > 0. The use of the check counter is
based upon the notion that this inequality will be evaluated in counter 72. Obviously, an end around
carry will occur when - |c| is added to t, if and only if the inequality holds. The coding for the check
procedure is :
OUT
IN
MISC.
621
8731
7
62
873
7
OUT
IN
MISC.
T
74
7
C
74
71
64
Check the quantity in ctr. C against the positive
tolerance in sw. or ctr. T.
where the code 64 is an automatic continue operation code if and only if an end around carry takes
place in the check counter. If t - jc| £0, no end around carry will take place, the machine will receive
no command to continue operation and will therefore stop.
X Storage Counter Relays
XI Multiply-Divtde and Functional Counters
DESCRIPTION OF THE CALCULATOR
21
FROM FIG 2
BUSS
TO FIG. 4
1 >-
PLUG BOARD
LOW ORDER
P-OUT RELAY
FROM FIG. 2
IN
RELAY
-^-i
READ-OUT
CAM
CONTACTS
TO FIG. 4
50 VOLT D.C.
Figure 3
The registers given over to multiplication and division are shown in Plate XI. While the counter
wheels and allied controls involved in these two operations are electrically interconnected, in such a
way that both multiplication and division cannot be carried on at the same time, the basic mode of
operation is better explained in terms of two separate schematic diagrams, Figs. 3 and 4. In the case
of multiplication, the multiplicand and the multiplier are read into the unit through in-relays connected
to the buss as in the case of the storage counters. The out-relay, however, through which the product
is read out of the multiply unit, connects to the buss through a plugboard provided to fix the decimal
point relation between the product counter and the buss.
The location of the decimal point is of no importance as far as the operation of the storage
counters is concerned. When the operating decimal point is assumed to lie between columns n and
n + 1 in the switches and storage counters, the corresponding decimal point in the product counter
will lie between columns 2n and 2n + 1 . Clearly, the product counter must contain forty -six columns
and the algebraic sign. Since only twenty-three of these columns and the algebraic sign may normally
22
DESCRIPTION OF THE CALCULATOR
OUT
IN
MISC.
654
761
52
431
7
t__ I i J_4-^ iL. 1 ii J™ AU- „.- ~£ 4-U^ ~1..,VU.-.^.*..4 xnmnniinln mnn^nnfu) fr\ motffl O CllltaWp
ue i"t;au uut iuiu uic uuaa, n its uic puipusc <ja uic pii^uuoiu, picviuuoij uicuumitu, «.u unu>.v, u. w — --—— -
selection of the columns to be read out based upon the location of the operating decimal point. The
plugging must be manually adjusted before the machine is placed in operation.
Since the coding for multiplication must select the multiplicand and multiplier and deliver the
product, it consists of three lines:
Multiply x in ctr. 56, code 654, by y in ctr. 18, code 52,
and deliver the product xy to ctr. 13, code 431.
There are no 7's in the Miscellaneous column of the lines of coding selecting the multiplicand and
multiplier and delivering them to the multiply unit. These are omitted because the code B 761, the
multiply code, is an automatic continue operation code and therefore replaces the 7's. No longer
does each line of coding correspond to a single operation of the machine. The first line of coding de-
livers the multiplicand to the multiply unit, and turns over control of the calculator to a subsidiary
sequence control within the multiply unit itself. The unit builds up and stores a multiplication table
consisting of the nine integer multiples of the multiplicand. The multiply unit then signals the sequence
control and calls for the multiplier. The process of multiplication is completed, within the unit, by
withdrawing such multiples of the multiplicand as may be indicated by the multiplier and adding them
together while shifting them to the proper columnar position. Upon completion of this summation,
control of the machine is turned back to the main sequence mechanism and the product delivered as
indicated by the third line of multiply coding.
In the event that one or both of the factors involved in a multiplication are negative numbers,
this fact is sensed and stored by the multiply unit. The factors are then treated as positive absolute
magnitudes for use in the multiplication. Finally the proper algebraic sign is appended to the product
and it is read out directly or inverted as required.
The buss is used during the multiplying operation only three times. If properly timed, other
operations involving the buss but not involving either multiplication or division may be carried on
during multiplication. Such operations are known as " interposed operations " and are considered in
23
DESCRIPTION OF THE CALCULATOR
detail under Multiplication in Chapter IV. Note that division as well as multiplication is excluded be-
cause, as previously mentioned, these operations are electrically interconnected.
When the operating decimal point of the calculator is assumed to lie between columns twenty-
three and twenty-four, the corresponding decimal point in the product counter will fall between column
forty-six and the algebraic sign. For this case, the multiply unit is equipped with a special out-relay
permitting the read-out of columns one through twenty-three of the product counter to the buss. The
normal multiplying operation, with suitable plugging, delivers columns twenty-four through forty-six
of the product counter to columns one through twenty-three of the buss as usual. The use of the special
low order product out-relay in effect provides the machine with forty -six column products as obtained
from twenty-three column factors. The coding for this operation is as follows:
Multiply x in ctr. 56, code 654, by y in ctr. 18, code 52,
and deliver forty-six columns of the product xy to ctrs.
69, 68, codes 731, 73.
Note that the line of coding dictating the low order product out must immediately follow the normal
product read-out in order to preserve the algebraic sign and deliver it to both counters receiving the
product.
One of the two pairs of ganged counters may be used in combination with this special product
read-out to build up the product of two quantities, either or both of which may consist of forty-six or
fewer digits. The error in such a multiplication will be less than or equal to 2.7 x 10" . Thus if the
quantity stored across counters A and B is multiplied by the quantity stored across counters C and D,
three multiplications, A x C, A x D, B x C, will be performed and the products summed in the ganged
counters. The product B x D is neglected since it is below the capacity of the machine. Examples of
the coding of such multiplications will be found under High Accuracy Computation in Chapter IV.
Although the organization of the multiply unit is far more complex than that of the storage counters ,
it is nevertheless possible to alter the multiplying circuits to permit special operations . For example,
it is sometimes required to print a function having a very wide range of values. In this case, it is
OUT
IN
MISC.
654
761
52
731
7
86
73
7
24
DESCRIPTION OF THE CALCULATOR
convenient to print a fixed number of significant figures together with an associated power often. The
"normalizing register", in conjunction with the multiply unit, accomplishes this purpose by shifting a
quantity so that its first significant digit appears in column twenty-three and recording the amount of
the shift. The amount of shift combined in a storage counter with a constant dependent upon the
position of the operating decimal point supplies the exponent required. Further examples of special
controls associated with the multiply unit will be described later in connection with the discussion of
the electro- mechanical tables of the elementary transcendental functions.
FROM FIG. 3
BUSS
TO FIG. 5
LOW ORDER
OUT RELAY
FROM FIG. 3
PLACE
fz-r-7=r»
— ^u U Uj
LIMITATION
DIVIDE
SWITCH
DIVIDE
UNIT
Od
IN
RELAY
READ- OUT
GAM
CONTACTS
TO FIG. 5
=»—
Rn wniT n r.
Figure 4
Division like multiplication requires three lines of coding. These read the divisor and dividend
into the divide unit and deliver the quotient to its specified destination using the connections shown
diagrammatically in Fig. 4.
25
DESCRIPTION OF THE CALCULATOR
OUT
IN
MISC.
3
76
21
31
7
Divide x in ctr. 3, code 21, by y in ctr. 4, code 3, and
deliver the quotient to ctr. 5, code 31.
After the divisor and dividend are read into the unit, they are shifted and stored so that their
first significant digits appear in the highest column of the registers in which they are stored. The
number of columns that the dividend was shifted and the complement on nine of the number of columns
the divisor was shifted are added together in the " Q-shift" counter. A constant dependent upon the
position of the operating decimal point is supplied to the Q-shift counter by a manually preset switch
known as the divide switch. Since the Q-shift counter is not equipped with an end around carry circuit,
the addition of a one in the units column completes the determination of the number of columns the
quotient must be shifted when it is read out into the buss in proper decimal position. A one added into
the units column of a counter to compensate for a missing end around carry is commonly known as an
"elusive one".
As soon as the divisor is delivered and control of the calculator turned over to the divide unit,
a table of the nine integer multiples of the divisor is built up and stored within the unit. When called
upon, the main sequence mechanism delivers the dividend. Under the subsidiary sequence control, the
multiples of the divisor are compared with the dividend and the largest multiple less than the dividend
selected. This multiple is then subtracted from the dividend while the digit defining it is entered in
the quotient counter. The process of division is continued in this manner, successively comparing,
subtracting and shifting to the right. Since the successive subtractions involve different columnar
positions of the dividend counter, an end around carry cannot be provided. The subtractions are ac-
complished by means of complements on nine together with elusive ones introduced into the units
column of each succeeding subtrahend. As the subtractions move to the right, ones appear on the left
since the multiples of the divisor consist of at most twenty-four columns and do not have sufficient
nines to the left to fill the dividend counter. However, when the digits of the remainders are selected
for comparison the extra ones are omitted. Assuming a six column machine, the subtractions appear
as follows:
26
DESCRIPTION OF THE CALCULATOR
213109
onAnn I KQiQonnnnnn 274 J RR392000000
45199
03591000000 - 54i
1
03592000000 359
972599
00851900000 - 274
1
00852000000 852
917799
10029990000 - 822.
1
10030000000 iPJL
972599
11002599000 - 271
1
11002600000 2600
753399
11010133990 - 2466
1_
11010134000 134
If, upon comparison, the calculator finds that all multiples of the divisor are greater than the dividend
or the remainder under consideration, a zero or "no-go" is entered in the quotient counter and a new
comparison made one column to the right. When the division is terminated, the dividend counter will
contain a series of ones and zeros and the last remainder.
Division may be terminated after any desired number of comparisons, by the place limitation
plugging and coding discussed under Division in Chapter IV. The number of significant digits in the
quotient will be either equal to the number of comparisons made or to this numberless one (if the first
comparison yields a no-go). Since the accuracy of the division is thus under control of the main sequence
mechanism it may be varied as desired within any given problem.
The quotient is read out into the buss through that part of the out-relay selected by the quantity
standing in the Q- shift counter. If a negative number is shifted to the right, the out- relay also supplies
the nines at the left required to complete the complement on nine of the quotient. The algebraic sign is
determined by the methods employed in the case of multiplication.
Further, as in multiplication, the buss is used only three times during division, and is otherwise
free for any interposed operations not involving either multiplication or division. It should now be
clear that many of the electro-mechanical operations necessary to multiplication and division are
27
DESCRIPTION OF THE CALCULATOR
identical. Indeed the calculator as constructed uses the same registers for both operations. These,
however, are controlled by two separate subsidiary sequence control systems, one for multiplication,
and one for division.
Though it is not immediately evident, division consumes almost four times as many cycles of
machine time as does multiplication and uses a great deal more apparatus. Clearly, then, this process
is to be avoided whenever possible. Fortunately, an iterative process based on the Newton Raphsonrule,
^-x^f^), n = 0, 1,2, ... (1)
is available for finding reciprocals. Let
f(x) = N - 1/x. (2)
Then x n+1 = x n (2 - NxJ, (3)
defines a sequence, x , which converges towards the reciprocal of N . Each succeeding application
of the iterative process roughly squares the error of the last preceding approximation.
Suppose that in a given computation the values of the independent variable increase in an arith-
metic sequence. Under these circumstances, the reciprocal of the nth value of the variable will furnish
a good first approximation to the reciprocal of the (n + l)st value. Thus the process of division may
be avoided with a considerable gain in the speed of computation. The application of equation (3) to the
Q
design of calculating machinery was first suggested by Aiken in 1938.
Equation (3) also provides the calculator with a means of dividing to an accuracy of forty -six
significant digits. The technique by which this is accomplished together with the techniques for ad-
dition, subtraction and multiplication, to the same accuracy, are described in the section on High
Accuracy Computation in Chapter IV.
The Newton Raphson rule, by proper choice of f(x) , may be made to yield an iterative process
for obtaining any fractional power of a given number so long as a suitable first approximation is avail-
able. This fact greatly extends the usefulness and speed of operation of the calculator without the
inclusion of a single special electrical circuit.
On the other hand, the computation of the elementary transcendental functions may not be dis-
posed of so easily. These require special registers as shown at the right of Plate XI, and make use
of the second panel of relays extending to the rear of the calculator.
28
DESCRIPTION OF THE CALCULATOR
rnum no. -r
BUSS
o o
o o
o o
PLUG BOARD
OUT
RELAY
FROM FIG. 4
LIO COUNTER
LOG COUNTER
MULTIPLY
DIVIDE
UNIT
LOGARITHM
UNIT
TABLE
RELAYS
50 VOLT D. C.
LOG
O
SWITCH
TO FIG. 6^
IN
RELAY
Or
READ-OUT
CAM
CONTACTS
TO FIG. 6
Figure 5
The method of computation of logarithms (Fig. 5) within the calculator depends upon two equations,
log (a«b«c« ...) - log a + log b + log c + ..., (4)
and
log (1 + h) - h - h 2 /2 + h 3 /3 - h 4 /4 + ... + (-i) n+1 h n /n +
.2 /o . u3 « k4 /a l ^ /_nn+i h* m * (5)
for h 2 < 1. The logarithm unit includes two counters known as the logarithm counter and the logarithm
in-out counter, together with a subsidiary sequence control which governs these counters in conjunction
with the multiply-divide unit. If it is desired to compute log 1() x,the coding in the main sequence con-
trol tape will read as follows
x lies in ctr. 39, code 6321, deliver log 1Q x to ctr. 8,
code 4.
OUT
IN
MISC.
6321
762
831
4
i
763
29
DESCRIPTION OF THE CALCULATOR
At the same time that x is read into the logarithm in-out counter, the code B 762 signals the logarithm
subsidiary sequence control to take over the direction of the calculator. From the logarithm in-out
counter, x is read to the logarithm counter so shifted that the first significant digit of x appears in
the twenty-third column of the logarithm counter. The amount of the shift is recorded and its comple-
ment on ten entered in columns twenty-two, twenty-three and twenty-four of the logarithm in-out
counter, in which the decimal point is now considered to lie between columns twenty-one and twenty-
two. The computation of the characteristic of x is then completed by adding 22 - n into the logarithm
in-out counter, the operating decimal point being between columns n and n + 1 . This quantity is sup-
plied by a manually preset constant register known as the logarithm switch. For example, if the
operating decimal point lies between columns fifteen and sixteen and x = 783.54210 50928 67954 , x is
shifted five columns to the left on reading from the logarithm in-out counter to the logarithm counter .
In this case, 22 - n = 7. Hence, the characteristic of x is computed as 995 + 007 = 002.
Now x = 7.83542 10509 28679 54 stands in the logarithm counter with the decimal point follow-
ing its first significant digit, and it is only necessary to compute the mantissa of log 10 x . This compu-
tation is perhaps best explained by a numerical example. Four successive divisions are performed:
x/7 = 1.11934 58644 18382 79142 85 ;
x/(7)(l.l) = 1.01758 71494 71257 08311 68 ;
x/(7)(l.l)(1.01) = 1.00751 20291 79462 45853 14 j
x/(7)(l.l)(1.01)(1.007) = 1.00050 84698 90230 84263 30 .
Equation (4) becomes
log 7.83542 10509 28679 54 = log 7 + log 1.1 + log 1.01 + log 1.007
+ log 1.00050 84698 90230 84263 30 . (6)
The logarithm table relays store logjQN accurate to twenty -one decimal places, for N equal to:
1.0
1.1
1.01
1.001
2.0
12
1.02
1.002
3.0
1.3
1.03
1.003
4.0
1.4
1.04
1.004
5.0
1.5
1.05
1.005
6.0
1.6
1.06
1.006
7.0
1.7
1.07
1.007
8.0
l.«
1.08
1.008
9.0
1.9
1.09
1.009 .
30
DESCRIPTION OF THE CALCULATOR
TVio in+a-.-i-iil lrvrr-iT.-i+1-irYi cfoniionnfi nnntpnlc oaloM- tho ■fnn'r 1 r%ero vi +h m c nalloH fnr Vwr thf> first fmir tpriTtS
on the right side of equation (6) and deliver them to the logarithm in-out counter for summation.
The last term of the logarithmic sum in equation (6) is of the form log (1 + a 10~ 4 ) where a < 10.
Writing (1 + a 10" 4 ) = 1 + h,
then h < 10~ 3 .
In using equation (5), six terms of the series are employed. Therefore, the remainder of the series
will be
R< h 7 (l + 7h/8 + 7h 2 /9 + 7h 3 /10 + ...)/7 ,
R< h 7 (l + h + h 2 + h 3 + ...)/7 ,
R< h 7 /7(l - h) .
R< 10" 21 /7(0.999) .
Clearly, the choice of four divisions and six terms of the series puts the error below the lower limit
of the capacity of the machine. The series given in equation (5) is used by the machine in the form
log 1Q (l + h) = ( ( ( ( (hc 6 + c 5 )h + c 4 )h + c 3 )h + c 2 )h + c^h ,
where c x = M, c 2 = -M/2, c g = M/3, c 4 = -M/4, c 5 = M/5, c g = -M/6;
M = log 1Q e .
The values of the c's are also stored in relays and supplied to the multiply unit as directed by the loga-
rithm sequence controls. One feature of these controls, not previously mentioned in this discussion,
permits the multiplicand, h, and its multiples to remain stored in the multiply -divide unit throughout
the evaluation of the series. This saves a considerable amount of machine time.
After summing all terms of equation (6) in the logarithm in-out counter, log 1Q x is read out into
the buss through plugging since it stands with its decimal point between columns twenty-one and twenty-
two and must be shifted to conform with the operating decimal position.
The exponential function, or anti-logarithm, is derived by a reversal of the process used to com-
pute logarithms. The method of computation is dependent upon the equations
10 x = 10 10a+b #10 c/10. 10 d/100 >10 e/1000. 10 f ^ ^
10 f = e h = 1 + h + h 2 /2'. + h 3 /3L + ... , (8)
where h = f log p 10 .
31
DESCRIPTION OF THE CALCULATOR
FROM FIG. 5
BUSS
TO Fl 6. 7
PLUG BOARD
OUT
RELAY
FROM FIG. 5
PLUG BOARD
IN
RELAY
O OO
ooo
o o o
EIO COUNTER
MULTIPLY
DIVIDE
UNIT
EXPONENTIAL
UNIT
TABLE RELAYS
Or
<J
READ- OUT
CAM
CONTACTS
TO FIG. 7
50 VOLT D- C
Figure 6
The exponential unit (Fig. 6) includes the exponential in-out counter and a subsidiary sequence
control governing this counter in connection with the multiply -divide unit. In order to compute 10 X ,
the main sequence control tape must read as follows:
x lies in ctr. 27, code 5421; deliver 10* to ctr. 20, code 53.
OUT
IN
MISC.
5421
7621
741
832
53
731
The code B 7621 signals the exponential sequence control to take over command of the calculator.
Simultaneously, x is read to the exponential in-out counter via the multiply unit, exponential -in plug-
ging and certain transformation circuits, which accomplish two purposes. First, a zero or nine is
read into the twenty-fourth column of the exponential in-out counter according as x is positive or
32
DESCRIPTION OF THE CALCULATOR
jli J it_ _ _1 1-.A_ 1 _* -. ;„ _~„J :_4.^ 4-U^ ~i-v„-v-^~±4.-.l in.W nnnntof on ehi-ftof? that thp
negative; secunu, uie ausuiuie vaiuc ui a ia ic<tu mnj mc cApucuuai m-um ^v»u»n.^..i ^v. ^,..**.*^~ - —
decimal point lies between columns twenty -one and twenty-two. Thus x stands in the exponential in-
out counter in the form :
column 24 23 22 21 20 19 18-1
digit + a b . c d e f
Columns one through eighteen of x are then multiplied by log e 10 and delivered to the multiply
unit for expansion in the series (8). The coefficients are stored in relays and sent to the multiply unit
as required. Again the multiplicand, h , is held constant while expanding the series in order to con-
serve machine time. Since h < 2.3 x 10" 3 , the remainder of the series will be
R » h 7 /7'. + h 8 /8'. + h 9 /9L + ... ,
R < h 7 (l + h/8 + h 2 /8.9 + „.)/7 ! . ,
R < h 7 (l + h + h 2 + h 3 + ...)/T. ,
R< h 7 /7'.(l - h) ,
R < (2.3) 7 x KT 21 /7'. (0.997) ,
R < 10" 2i .
Clearly, the use of seven terms of the series leaves a remainder which is below the capacity of
the machine.
The quantities ,
10 o.o 10 o.oo 10 o.ooo
00.1 iqO.01 10 o.ooi
qO- 2 10 - 02 10 - 002
00.3 IqO.03 10 0.003
\° 0A \° Q 0.0A 10 0.004
Jn0.5 i"0.05 in 0.005
1q0.6 io0.06 JoO.006
inu.i 10"""' 1U "
io°- 8 o - 08 io - 008
io - 9 io - 09 IO ' 009 '
are stored in table relays accurate to twenty -one decimal places. The proper values are called for by
columns nineteen, twenty and twenty-one of x as it stands in the exponential in -out counter so that the
r. 1 nC/10 1 n d/100 , n e/1000 J
product. P = 10 ' «10 ' -10 -KT ,
may be formed.
33
DESCRIPTION OF THE CALCULATOR
This product, P, will stand in the product counter with its decimal point between columns forty-
two and forty-three. If x is a positive quantity, the product is read out to a forty-five column plug-
board in which the decimal point is assumed to lie between columns twenty-one and twenty-two. This
read-out is accomplished through a multiple out-relay, the proper part of which is selected by the
quantity 10a + b standing in columns twenty -two and twenty -three of the exponential in-out counter.
From the plugboard, the product passes to the buss at the operating decimal position through manually
preset plugwires connecting the plugboard to the buss in proper columnar relation, and thence to the
storage register indicated by the third line of exponential coding.
If x is a negative quantity, the reciprocal of the product, P , is obtained by the divide unit as
ordered by the exponential sequence control. The reciprocal is then read out of the quotient counter
to the storage register by circuits equivalent to those employed in the case in which x is positive.
The third electro-mechanical table contained within the calculator is that of the function, sin x .
The method of computing sin x is based upon the equations:
sin (- x) = - sin x ; (9)
sin (x + 2n t ) = sin x ; (10)
sin x = cos (-ir/2 - x) ; (11)
sin x = x - x 3 /3l + x 5 /5l - x 1 /!'. + ...
+ (- l) n x 2n+1 /(2n + 1)1 + ... , n = 1, 2, 3, ..., 10 ; (12)
cos x = 1 - x 2 /2i + x 4 /4'. - x 6 /6'. + ...
+ (- l) n x 2n /(2n)L + ... , n = 1, 2, 3, ..., 10 . (13)
Since the series (12) and (13) are alternating series the remainder, R, will be less than the first term
omitted. Assuming x < ir/A,
|R| <U/4) 22 /22l .
Taking the logarithm of both sides of the inequality,
log 1() |R| < 22(log 10 Tr - log 1() 4) - log 1() (22'.)
< 22(0.498 - 0.602) - 21.050 < - 23 .
Thus |R| < 10 and the error in using these series for computation falls below the capacity of the
calculator.
34
DESCRIPTION OF THE CALCULATOR
FROM FIG. 6
BUSS
o o o
o o o
o o o
PLUG BOARD
PLUG BOARDS
u
OUT
RELAY
t
FROM FIG. 6
SIO COUNTER
MULTIPLY
DIVIDE
UNIT
SINE
UNIT
TABLE RELAYS
Ci
IN
RELAY
o o o
o o o
o o o
J
oJ
TO FIG. 8
O O O
O O O
O O O
] /Z-a- RELAY
READ -OUT
CAM
CONTACTS
Ct
TO FIG. 8
50 VOLT D.C.
Figure 7
The sine unit (Fig. 7) is composed of the sine in-out counter and subsidiary sequence circuits
having control of this counter, the multiply unit and certain table relays providing the coefficients of
the series together with other necessary constants such as r/4, r/2, ± * and 2v . The main
sequence control tape dictates the computation of sin x by the coding:
x lies in ctr. 14, code 432; deliver sin x to ctr. 40,
code 64.
In order to compute sin x, it must first be determined in which quadrant x falls. The first
operation in the sine sequence multiplies x by 1/2 ir (supplied by a relay through plugging) at the
operating decimal position. Then the product |x| /2 ir is read into columns one through twenty -three
of the sine in-out counter with decimal point at the operating position. At the same time, the algebraic
OUT
IN
MISC.
432
7631
84
64
7
7321
35
DESCRIPTION OF THE CALCULATOR
sign of x is read into the twenty -fourth column of the sine in-out counter. Let jxj/2rr indicate
|x| /2ir with its integral part omitted. This integral part represents multiples of 2ir which may be
dropped by virtue of equation (10). Through plugging, |xl/2 ir is next read from the sine in-out
counter to the multiplicand counter so shifted that its decimal point lies between columns twenty-two
and twenty-three. The algebraic sign of x remains stored in the sine in-out counter. The integer
four, supplied by a table relay, is read to the multiplier counter." The resulting product is read into
the sine in-out counter with its decimal point between columns twenty-two and twenty -three. Four
cases may now be distinguished:
(a) 0<2|x|/r< 1, | x| in quadrant I, sin|x|>0;
(j3) 1 <2|x|/7r < 2, |x| in quadrant II, sin |x|> 0;
(1) 2<2|x|/7T<3, |x| in quadrant III, sin |x|£ 0;
( &) 3 <2|x|/7T <4, |x|in quadrant IV, sin|xl<0.
Which of these four cases appertain in the case of a specific value of x maybe determined by sensing
the integer in the twenty-third column of the sine in-out counter. The value of this integer together
with the algebraic sign of x previously stored in the twenty -fourth .column of the sine in-out counter
complete the determination of the sign of sin x .
The procedure by which this is accomplished and by which x is reduced to a first quadrant angle
will now be discussed. The quantity 2 |x| /rr is multiplied by TT/2 and when this operation is com-
pleted, the product, |x| , is read into the sine in-out counter. During this multiplication, the sensing
circuits on column twenty -three of the sine in-out counter order the following operations:
(1) Reset all columns but the twenty-fourth of the sine in-out counter;
(2) Case (a): £ |x| < ir/2
|x| is read into the sine in-out counter directly;
Case (£): if/2 £ |x| < *
|x| is inverted when read into the sine in-out counter,
ir is added into the sine in-out counter;
36
DESCRIPTION OF THE CALCULATOR
Case (-(): 1T £ jxj < 3 if/2
|x| is read into the sine in-out counter directly,
- if is added into the sine in-out counter,
a nine is added into the twenty-fourth column of the sine in-out counter;
Case(S): 3 ir/2 <|x| < 2ir
|x| is inverted when read into the sine in-out counter,
2 r is added into the sine in-out counter,
a nine is added into the twenty -fourth column of the sine in-out counter.
Since the sine in-out counter has no end around carry, and since any digit other than a nine in the
i~, A ^* ? ras „±>, ™\-,-, mn .-.* thic rnnntpr is the eauivalent of a zero, the final algebraic sign of sin x now
stands in the twenty-fourth column of the sine in-out counter. The reduced first quadrant angle, X,
corresponding to the given value of x stands in the remaining columns.
Two cases remain to be distinguished:
(a) < X < 7T/4;
(b) 7T/4<X < IT/2.
FROM FIG. 7
O O O
O O O
O O O
PLUG BOARD
L— o
OUT
RELAY
L
FROM FIG. 7
BUSS
LiO COUNTER |
I . -J
Otr
IN
RELAY
READ -OUT
CAM
CONTACTS
50 VOLT D,C
TO FIG. 9
-— t
TO FiG. 3
Figure 8
37
DESCRIPTION OF THE CALCULATOR
After a sensing circuit has compared the value of X with r/4, in case (a), the computation proceeds
by evaluating the series (12). In case (b), if /I - X is formed and the series (13) is evaluated. In
either case, the result of the summation of the series is delivered to the sine in-out counter, columns
one through twenty-three, with the result that this counter then contains | sin x | and the appropriate
algebraic sign.
The read-out of sin x to the buss for delivery to storage is through plugging, in order to shift
the function to conform to the operating decimal position. The read-out is direct or inverted accord-
ing as zero or eight on the one hand, or a nine on the other hand, stands in the twenty-fourth column
of the sine in-out counter.
The logarithm in-out counter and the sine in-out counter are commonly used as "shift counters".
These counters are equipped with pluggable and direct read-ins and read-outs as shown in Figs. 8 and
9. They may be used to multiply or divide by powers of ten. In addition, the pluggable read-outs may
be manually so adjusted as to permit selective read-out of the shift counters by means of which any
FROM FIG. 8
O O O
O O O
O O O
O O O
O O O
O O O
PLUG
BOARD
FROM FIG. 8
OUT
RELAYS
t—
BUSS
TO FIG. 10
PLUG BOARD
SIO COUNTER
cd
IN
RELAYS
o o o
o o o
o o o
READ- OUT
CAM
CONTACTS
50 VOLT D. C.
U
TO FIG. 10
Figure 9
38
DESCRIPTION OF THE CALCULATOR
!.. — _,. _~~.. 1~~ ^»liT. n ./.J +<■> +V.^% Vv,,^o. mViilo fKa -»»a»v»oiriirinr 94 _ to uto oimnrpfiSpH This RftleCtiVe
III UUiUUlIia UiCty UC UCX1VC1CU W UlC UUOO WllUl- UH»^ 1 ^unniiu.f, — * "x *** v. ^— ^^* — ^~— . ^..—
read-out does not erase any part of the number standing in the shift counter. The read-ins and read-
outs of these two counters have been placed under control of the main sequence mechanism by codes
which are independent of the codes of the functional units of which the shift counters are themselves
a part. Since the logarithm in-out and sine in-out counters do not have complete carry circuits at
all times, and have codes and resets which differ materially from those of other registers, they must
be used with care. A detailed discussion of these codes and their uses will be found in Chapter IV.
With the aid of the electro-mechanical tables of log 1Q x , 10* and sin x , all of the elementary
transcendental functions, including the hyperbolic functions, may be obtained through the use of the
operations of the calculator already described. In order to provide for inverse trigonometric functions,
higher transcendental functions and empirical functions defined by tabular data, the calculator is
equipped with three mechanical interpolators.
The three interpolator mechanisms and their accompanying switches are shown in Plate XII, to
the left of the main sequence mechanism. The three units share in common the interpolation counter
and the interpolation check counter, (Fig. 10). A function is introduced into an interpolation mechanism
in the form of a perforated paper tape, (Plate Xm). This tape is similar to the main sequence control
tape, but in place of commands to the calculator, contains coded successive equidistant values of the
argument, each accompanied by the necessary interpolation coefficients. Any order of interpolation
up to and including the eleventh may be employed.
The coding for interpolation by unit I as it appears in the main sequence control tape is:
x lies in ctr. 50, code 652; a tape containing f(x) is on
Interpolator I; determine f(x) and deliver it to ctr. 51,
code 6521.
OUT
IN
MISC.
652
7654
62
841
652
763
6521
73
7
There are a very great many possible variations in this coding as well as in the possible uses of the
XII Sequence Control Mechanism and Interpolators
XIII Interpolator
39
FROM FIG. 9
DESCRIPTION OF THE CALCULATOR
BUSS
TO FIG. II.
OOO
OOO
OOO
OOO
oo o
OOO
H 1
PLUG BOARDS
OUT
RELAY
OUT
RELAY
l_Li
PLUG BOARDS
IN
RELAY
OOO
OOO
OOO
INTERPOLATION
COMPUTING CIRCUITS
MULTI PLY
DIVIDE
UNIT
'C" SW. ©
INTERPOLATOR
MECHANISM
FORWARD CLUTCH
REVERSE CLUTCH
TAPE SENSING PINS
INTERPOLATION
POSITIONING CIRCUITS
"a/2" sw.0
INTERP. CTR.
INTERP. CK. CTR. I "C" SW.
Ci
-J
t
IN
RELAY
+-J
CAM
CONTACTS
50 VOLT D. C.
READ -OUT
CAM
CONTACTS
Cji
Figure 10
OOO
OOO
OOO
3D
40
DESCRIPTION OF THE CALCULATOR
_._ i __..-_j_i ii.„ An »nk nnnn ,ki n i. k^tra hoon HoxroionpH nn tn thp nrpsent time are included in Chap-
imerpuiatui" uiiile>. fliiuiuiuocnmvuiimK m^^,.» v.-^.^-^ — c — — * —
ter IV. The present discussion will be confined to the most elementary case, that of interpolation by
means of Taylor's series.
A function f(x) is to be determined. The independent variable, x, is considered as consisting
of two parts, x = a + h, where a is an integral multiple of a power of ten. Since four columns are
provided for containing the value of a , it is clear that a functional tape may contain 10 arguments.
An interpolation is performed by evaluating the series,
f(x) = f(a + h)
= f(a) + f'(a)h + f"(a)h 2 /2'. + ... (14)
= c rt + c,h + c^h^ + c„h 3 + ...,
in the form ,
f(x) = f(a + h) = ((((... + c 4 )h + c g )h + c^h + c^h + c Q . (15)
The interpolation process maybe divided into two distinct parts. The first consists of position-
ing the functional tape and the second of the computation necessary to the interpolation itself. For
tape positioning, the argument, a, and the highest order column of h are delivered to the interpolation
counter. The interpolator mechanism first reads the tape to discover the position at which the tape is
standing. By subtraction in the interpolation counter, the number of arguments the mechanism must
pass over in order to arrive at the required argument is determined. To accomplish tape positioning
in the shortest possible time, functional tapes are made endless. Suitable sensing circuits aided by
manually preset switches direct the mechanism to move the tape in the direction of shorter travel.
The highest order column of h is combined with a half- correction in the interpolation counter to in-
sure positioning to the nearest argument. As the tape steps, the number of arguments to be covered
(stored in the interpolation counter) is reduced one for each argument passed and is finally reduced
to zero.
At the beginning of the positioning operation the required argument, a, is read into the interpo-
lation check counter. At the end of the positioning operation it is transferred to the interpolation
counter and used to checkthe position of the tape. K the tape is not in proper position because an im-
possible argument has been sent to the interpolation unit or because of faulty mechanical operation,
41
DESCRIPTION OF THE CALCULATOR
the positioning mechanism will try a second time to find the required argument. The calculator is
stopped and a red light turned on in the event that the positioning mechanism fails on this second try.
However, if the tape is found to be in the required position, the interpolation sequence control
takes over command of the calculator. The quantity x is again read out of storage into the buss and
the h part delivered by plugging to the multiply unit. Suitable corrections of h , such as nines to the
left if h is negative, are also made by plugging.
The interpolation sequence control then evaluates series (15), while the multiplicand, h, is held
constant as usual to conserve machine time. The coefficients, c , c j, ..., Cp e Q ,are read out of
the functional tape and added into the multiplier counter under control of the interpolation sequence
circuits.
When a relatively large number of values, such as constants or random values of a variable,
are to be used by the calculator, and further when these values are to be used in a prescribed order,
they may be supplied to the machine via one of the interpolator mechanisms and a perforated paper
tape. Such a tape is known as a "value tape" to distinguish it from a functional tape. Mathematically,
the operation of reading from a value tape is the equivalent of zero order interpolation. In order to
increase the flexibility of the interpolators when used in this manner, three sequence codes have been
assigned to each interpolator mechanism. These require that the tape be stepped forward, stepped
back and that the sensing pins read from the tape (Fig. 11), as in the following examples for interpo-
lator I.
Step the tape forward.
Step the tape back.
Read the value from the tape to ctr. 34, code 62.
The codes for accomplishing the same purposes in connection with interpolators n and m may be
found in the section on Interpolators in Chapter IV.
OUT
IN
MISC.
753
|
754
85
7
62
7
42
FROM FIG- 10
DESCRIPTION OF THE CALCULATOR
DU35
TO FIG- 12
O O O
O O O
O O O
PLUG BOARD
OUT
RELAY
OUT
RELAY
t_
CARD FEED
v^_^_L
FROM FIG. 10
NTERPOLATOR
VALUE TAPE
" READ-OUT -l,
CAM QJI
rnwTAr.TC
TO FIG. 12
50 VOLT D. C.
Figure 11
Gtiier means of supplying data to the calculator are the two card feeds shown in Plate XIV and
Fig. 11. These employ standard tabulating machine cards and have three advantages over the value
tape. First, since tabulating machines are highly standardized, the cards permit the interchange of
data from one computation laboratory to another. Second, the devices required in the manual prepa-
ration of the cards have been developed to a high degree of perfection. Third, the calculator is itself
6(juipp6u win! a card punching mechanism.
The disadvantage of punched cards as compared to a value tape lies in the fact that the card feeds
must accept the cards in the order in which the deck is stacked. No provision is made for retrieving
a card once it has passed through the feed. Hence, a second use of the value punched in a card requires
the intervention of an operator.
The coding for reading from card feed I is:
OUT
IN
MISC.
21
7632
Read the value from the card in feed I to ctr. 3, code 21.
When using punched cards and value tapes, the coding must be arranged to synchronize their reading
XIV Typewriters, Card Feeds and Card Punch
XV Tape Punch
43
DESCRIPTION OF THE CALCULATOR
/
units with the main control tape. This implies that suitable operating instructions must be prepared
to insure that cards and fcalue tapes are properly inserted in the calculator.
A control is provided on each card feed to stop the calculator when the cards are exhausted or
jammed. The quantities in the cards are read into the buss through plugging and therefore may be
shifted to conform with the operating decimal position. This is not true, however, of value tapes.
Occasionally a problem is so voluminous as to tax the facilities of the calculator . In such cases,
the main control tapes are so designed that the computation may proceed part way, the intermediate
results may be punched into cards and the cards later fed into the calculator for further computation
under the direction of a second main control tape.
The card feeds and interpolator mechanisms together with the switches previously described
represent the means by which numbers may be introduced into the calculator as a basis for compu-
tation. For recording computed results, two methods are available, the card punch mentioned in the
previous paragraph and two automatic typewriters, (Plate XV).
The printing and punching of numbers is accomplished with the aid of registers known as the
"print" and "punch" counters together with special circuits designed to control the recording devices.
The print and punch counters (Fig. 12) are equipped with in- and out-relays and complete carry
circuits so that they may function as standard storage counters in addition to performing their special
purposes .
The coding for the printing operation consists of two lines, one line to read the quantity to be
printed to the print counter and one to initiate the printing operation.
x lies in ctr. 18, code 52; print x on typewriter I.
The controls of the typewriters are very flexible with respect to the number of digits printed,
their spacing, columnar position and line spacing. These controls are considered in detail under Print-
ing in Chapters IV and V. The computed results may be reproduced photographically directly from the
typewritten sheets . This avoids the possibility of error due to copying, inherent in most compu-
tational procedures.
OUT
IN
MISC.
52
7432
752
7
44
FROM FIG. 1 1
DESCRIPTION OF THE CALCULATOR
BUSS
OUT
RELAYS
t .
o o o
o o o
o o o
PLUG
BOARD
FROM FIG. II
PUNCH
COUNTER
IN
RELAYS
OUT
RELAYS
"T .
PUNCH
o o o
o o o
o o o
PLUG
BOARD
PRINT
COUNTER
IN
RELAYS
TYPEWRITER
♦ READ-OUT
CAM
CONTACTS
TO FIG. I
)KJ VULI U. U.
The punch coding also consists of two lines, one line to read into the punch counter and one to
initiate the punching operation.
x lies in ctr. 37, code 631; punch x into a card.
In order to avoid the loss of computed results, the card punch is equipped with a stop control which
prevents a read-in to the punch counter, stops the calculator and lights a red signal light in the event
that a blank card is not in the proper punching position at the time the sequence control tape dictates
the punching operation.
Not all problems imposed on the calculator require the use of punched cards. Hence, a manual
keyboard connected with the punch maybe used for the preparation of cards while the calculator is in
OUT
IN
MISC.
631
753
1
1
75
45
DESCRIPTION OF THE CALCULATOR
operation. This punch, however, does not produce any of the tapes used by the machine. It will be
recalled that the Jacquard weavers laced their cards together to provide the tapes they required for
the control of their looms. The calculator, on the other hand, uses smooth tapes prepared by means
of a specially designed manual punch shown in Plate XV.
Two keyboards are used interchangeably to control this punch. The first of these is used in the
preparation of functional and value tapes. It has twenty-four columnar positions and perforates the
tape in such a way as to represent any one of the ten digits in each column of a twenty-three figure
number together with the algebraic sign. A four line code is used as shown in Fig. 13. This figure
must be read from the bottom to the top, representing the forward direction in which the tape passes
through the reading mechanisms of the interpolator units .
In general, a value tape consists of a tabulation of constants punched into the tape in a given order.
A functional tape, in contrast, contains a group of entries associated with each argument. The first
entry in each group is the argument itself. This is followed by the interpolational coefficients, c n ,
c .., ..., Cp Cq, in this order as shown in Fig. 14.
The argument must be punched in columns fifteen, sixteen, seventeen and eighteen of the tape
regardless of the location of either the tape decimal point or the operating decimal point. The nega-
tive algebraic sign, if required, must be represented by a nine in the twenty-fourth column. Each
argument must be identified by an argument code consisting of a three-four punched in the first
column of argument punching. Fig. 14 represents a portion of a tape for fourth order interpolation on
f (x) = tan x with an accuracy of twelve decimal places . The figure illustrates all of the salient features
of an interpolation tape.
The main control tapes are punched by the second keyboard, previously mentioned, which ap-
pears in Plate XV. It is designed to contain two lines of coding which must be punched simultaneously.
This is necessary because the sequence and interpolator mechanisms, though radically different in
operation, are in reality made of the same mechanical components . One numerical value in a functional
tape occupies the same amount of space as two lines of control tape coding. The device of setting up
two lines of control tape coding per punching operation makes it possible to punch sequence control
tapes and functional tapes with one and the same manual punch.
46
DESCRIPTION OF THE CALCULATOR
•• •
_j^ fy_
v&TTnr vim
•
••
• #
•
•••
•
•••
• • • • #
• • • • •• •
• •• • ••••#
••• •••• ••
• •
•••
• • • •
• • •
• •
• • •
•
•
•
•
m « # m * •
• • • • •
• ••••••
••• • • ••
•
• #
•
•••
•••
•••
•••
•••
1 •«•
• ••
• ••
•••
••• •••
•••
1 •••
••• •••
• ••
«#•
•••
•••
• ••
• ••
-
1 •••
•••
• ••
• ••
•••
nfy V-
Negative Argument -51
Argument Code in 1st col.
Positive Argument 51
Argument Code in 1st col.
Negative Number
-698 321 576 438 499 013 451
Positive Number
521 328 794 532 605 972 100 28
Diagonal Number
012 345 678 901 234 567 890 123
000 111 222 333 999 999 999 99
999 000 111 222 888 888 888 88
888 999 000 111 777 777 777 77
777 888 999 000 666 666 666 66
666 777 888 999 555 555 555 55
555 666 777 888 444 444 444 44
444 555 666 777 333 333 333 33
333 444 555 666 222 222 222 22
222 333 444 555 111 111 111 11
111 222 333 444 000 000 000 00
Figure 13
DESCRIPTION OF THE CALCULATOR
47
-A Ar
• ••
• ••• •
• • •
•• •••
•• • •
•• ••
•• •••
• • • •
• • • •
•• •• •••
•• • • •
• • ••
••••••
•••
••• •• •
»• • •
• • • •
• • • ••••
• • •
• • •
•••• • •
•••••• ••
• • •
• •
• • • •
•• • •• •
• • •
• • • •
• • • •
• • • •••
• • •
• • •••
••• •
• • ••
• ••
-^ <v
FUNCTIONAL TAPE
C3 0.503 529 133 009
C 4 0.300 041 586 295
Arg 0.33
Co 0.331 389 405 224
Ci 1.109 818 937 895
C2 0.367 782 237 736
C3 0.491 818 782 980
C4 0.285 577 613 215
Arg 0.32
C 0.320 327 505 078
Cx 1.102 609 710 509
C 2 0.353 196 217 642
C3 0.480 675 033 370
C4 0.271 705 506 740
Arg 0.31
Figure 14
48
DESCRIPTION OF THE CALCULATOR
I
*»
• • •
• •
••• •
•
• •
• •••
• ••
•••
• •• •
**e **
9 •
• •• •
••
• «
•
•
•• •
• ••
*
• • •• •
• •
• •
•
••
••
• ••
• •• •
g Q 09
• •
•
• • •
••
•• •
• •
• ••
• •
• • •
•• *
•
•
*
99
•
•• *
w SS
m m
• •
• •
• • •
• •
• ••
•
START
••
1
vv
n
OUT
74
21
32
7432
321
321
IN
74
74
321
321
321
761
321
MISC.
64
71
7
7
732
7
752
21
7432
7421
74
7
31
7
3
21
32
321
321
7
31
rti.1
1 i
3
32
732
U J*.
1
n
743
32
742
21
7
1
7
2
21
2
21
7
1
761
7 i
2
7
32
32
741
1
7
1
761
START
87
Figure 15
DESCRIPTION OF THE CALCULATOR
CODING SHEET
49
OPERATION
Xjj.^ to MC
ax to MP and to ctr. lj ctr. 1 ■ x^
reset ctr. 6
x^Ax to ctr. 2
x n to MC
Xjj^Ax to ctr. 3
Xn-1 AX to ctr. 3
x n to MP
(Ax) 2 to ctr. 3
1 to ctr. 6
x n 2 to ctr. 4; turn on typewriter I
-x^ to ctr. 6; ctr. 6 = 1- x n 2
V V 1 - Xn.! 2 to
MC
reset ctr. 7
-x n 2 to ctr. 3
1/V 1 - x^! 2 to
HP
tolerance to check ctr.
check to print ctr. I
print on typewriter I
1/(1 - Xn.! 2 ) to ctr. 7
-1/(1 - x n _i 2 ) to MC
reset ctr. 7
3 to ctr. 7
1 - Xj/ to MP
(1 - Xn 2 )/(1 - x n _i 2 ) to ctr. 7
check to check ctr.
check and reset check ctr.
LINE
10
20
OUT
741
32
742
743
872
31
321
31
7421
21
321
IN
761
32
761
21
21
21
32
32
761
321
21
74
7432
752
321
761
321
321
7432
32
21
74
321
321
74
74
MISC.
732
32
732
71
64
Figure 16
50
DESCRIPTION OF THE CALCULATOR
w ik ^hsv^rrr. o cKm4 oooti™ nt nnntTTti tanp and 'Pia. 1fi. the r.orresr.ondiner coding?. As in
the case of value and functional tapes, the control tape must be read upwards.
Since the control tapes deal with operations only, they represent the solution of a mathematical
situation independent of the values of the parameters involved. Hence, such control tapes as are of
general application are preserved in the tape library for future use. Functional and value tapes of
general interest are likewise preserved.
When a problem is referred to the Computation Laboratory, the first step in its solution is that
taken by the mathematician who chooses the numerical method best adapted to computation by the cal-
culator. This choice is made on the basis of the accuracy desired, the possible checking operations
and the speed of computation. Such functional, value and control tapes as are required are then com-
puted, coded and punched. Since the mathematician cannot always be present while the calculator is
running, instructions must be prepared to guide the operating staff. These must include switch settings,
the list of tapes to be used, plugging instructions, manual resets, information concerning checks,
starting, stopping and rerun instructions. The instructions for the plugging of the functional units
are usually given in the form of diagrams similar to those in Chapter V. The manual resets may in-
clude the clearing of both functional and storage counters. On the functional panel, (Plate XI), may
be seen the push-buttons by which all of the functional counters maybe reset except the forty-seventh
or sign column of the product-quotient counter which is reset at the end of each multiplying or di-
viding operation. Above the sequence mechanism are the seventy-two push-buttons which permit
manual resetting of each of the storage counters. Directly below the reset buttons and above the
sequence mechanism, (Plate XIT), is a constant register which exactly duplicates one of the sixty
switches. Because this register is frequently used to provide the increment of the independent variable,
it is known as the independent variable switch. Further, because it is located conveniently near the
sequence mechanism, this switch is particularly useful in testing the various units of the calculator.
The start and stop keys are located directly above the sequence mechanism as shown in Plate XII.
The use of these keys and their associated electrical circuits will be discussed in Chapter III.
The main sequence control is equipped to advance the tape, step by step, normally at a rate of
200 steps per minute, unless one of the subsidiary sequence controls is directed by the coding to
51
DESCRIPTION OF THE CALCULATOR
temporarily take over command of the calculator. In this case, the control tape is stopped until the
subsidiary sequence control has finished its operation and signals the main sequence control to con-
tinue operation.
The normal step rate of the sequence tape, then, does not give a good estimate of the speed of
the calculator. This may be better given by citing the time required for various operations. When
computing with twenty-three significant digits and operating decimal point between columns fifteen
sixteen, the maximum operation times are as shown in the following table.
Operation
Seconds
Cycles
Addition
0.3
1
Subtraction
0.3
1
Multiplication
6.0
20
Division
11.4
38
Log 1Q x
68.4
228
io x
61.2
204
Sinx
60.0
199
All of the times cited include the time required to transfer the arguments to the functional units and to
deliver the results for further computation. The time required for all operations, except addition and
subtraction, may be shortened by reducing the accuracy of the computation. Obviously, the only way
to state the relative speed of the calculator is to solve a problem first by manual methods and then by
use of the machine. Such an estimate has been made and apparently the machine is well nigh one
hundred times as fast as a well equipped manual computer. When it is borne in mind that a computer
can work little more than six hours a day before fatigue causes him to produce a prohibitive number
of errors, it becomes clear that operating on a twenty-four hour schedule, the calculator may produce
as much as six months work in a single day.
52
DESCRIPTION OF THE CALCULATOR
References
1. E. T. Whittaker and G. Robinson, Calculus of Observations (3rd ed.) (1940), p. 2.
2. Whittaker and Robinson, loc. cit,
3. F. Cajori, History of Mathematics (1919), p. 226.
4. Whittaker and Robinson, op. cit., chap. Vn.
5. Whittaker and Robinson, op. cit., p. 363.
6. Whittaker and Robinson, op. cit., p. 367.
7. Whittaker and Robinson, loc. cit.
8. H. H. Aiken, Proposed Automatic Calculating Machine (1937), p. 18, (privately distributed).
q ti xi Aiken- Harvard Lecture Notes on Applied Mathematics (1938). p* 10.
53
CHAPTER HI
ELECTRICAL CIRCUITS
"Simplicity is Nature's first step, and the last of Art."
Philip James Bailey
In the preceding chapter, means were described by which the Automatic Sequence Controlled
Calculator is kept in continuous operation. However, no mention was made of the circuits by which
the machine is started and stopped. This subject may best be approached by consideration of the main
sequence control.
Figures 17 and 18 show the sequencing circuits of a machine having nine reading pins, three in
each of the A, B and C groups, rather than the twenty-four pins of the calculator. The nine reading
pins are numbered 6, 7 and 8 in each group in order that the starting and stopping circuits may be
presented in a manner consistent not only with the diagrams, but also with the calculator itself. The
nine reading pins make available 2 9 possible orders per line of coding and are sufficient to develop
all the ideas necessary to a clear understanding of the sequence control. An attempt to draw the actual
circuits employed in the calculator would lead to inconveniently large and complex diagrams .
Figure 17 shows the reading contacts controlled by the reading pins and the tape, neither of the
latter being shown in the figure. Once the pins have advanced against the tape and closed the reading
contacts in positions corresponding to the holes in the tape, an electrical circuit is established to ener-
gize the sequence relays. Suppose a line of coding to read (6, 6, 7) corresponding to the reset of
counter 32, code 6. Then beginning at the positive terminal of the generator, assuming the cam con-
trolled contact FC-101 to be closed and for the moment further assuming that the four -pole read relay
contacts are closed, complete circuits exist through the reading contacts A-6, B-6, C-7, through the
corresponding sequence relays to the negative generator terminal. When the sequence relays are
picked up, each is held in its energized position through one of its own contacts and the cam controlled
contact FC- 102.
The sequence relays are multipolar, and in addition to their hold contacts, have "cascade" con-
tacts wired as shown in Fig. 18. These permit the selection of out-, in- and miscellaneous relays
54
ELECTRICAL CIRCUITS
+ 50 VOLT D.C.
FC-IOI
CM
FC-102
CM
OUT- A
READING CONTACTS
IN-B
READ- 1,2,3,4
MM
r r r r
MISC. -C
/, *
.r
A-6
i!±
T
A
T
r
Js-6 J^-4 Je-4 Je-6 J^-4 Jl-4 _ jVs J^-4 J^-4
A™ C« I
-6P B-7P
T
T
JJ — H(
ini
T
C"8
SEQUENCE
RELAYS
-50 VOLT D.C.
ngure n
which are picked up by means of cam controlled impulses. The multipole relays are of the double
throw variety, having four, six or twelve poles, and may be either single or double coil. They are
jack connected and wired with the aid of plug-in wires as shown in Plate XVI. When a relay is not
energized, circuits may be completed through its normally closed (NC) contacts. On the other hand,
when a relay is picked up, circuits may be completed through its normally open (NO) contacts. Thus
any code corresponds to a series of normally open and normally closed sequence relay contacts . For
example, as may be seen in Fig. 18, the in-relay of counter 32, code 6, is picked up through B-8-1 NC,
B-7-1 NC and B-6-1 NO. A complete tabulation of the cascade contacts for all of the codes at present
used by the calculator is given in Appendix I.
The contacts of the out-, in- and miscellaneous relays are not shown in Fig. 18 as these are
parts of the circuits to be controlled by these relays rather than of the sequence control circuits.
XVI Relays and Cam
K
H
A
w
/
m
O L
XVU Storage Counter
55
ELECTRICAL CIRCUITS
50 VOLT D.C.
Ci
FC-CAM-A
Ci
FC-CAM-B
FC-CAM-C
A-8-1
n
1
B-8-1
n
Ci
6
C-8-1
A-7-1
A- 7- 2
1
B-7-1 I B-7-2 C-7-1 C-7-2
A-6-1
A-6-2
A- 6-3
A-6-4
B-6-1
B-6-2
B-6-3
B-6-4
C-6-1
C-6-2
C-6-3
C-6-4
&mU &4UU &U&£
50 VOLT D.C.
IN -RELAYS AND
OUT- RELAYS SUBSIDIARY SEQUENCE MISCELLANEOUS RELAYS
CONTROLS
Figure 18
READING PINS ADVANCED
READING CONTACTS MADE
READ RELAY FC-105
SEQUENCE RELAYS FC-IOI, 102
OUT- RELAYS FC-A
IN- RELAYS FC-B
MISCELLANEOUS RELAYS FC-C
CLUTCH MAGNET FC-105
TAPE MOVES FORWARD
ONE CYCLE
Figure 19
56
ELECTRICAL CIRCUITS
FC-iOS
/
START
KEY
rl ^ C:
J
FC-103
CM
REPEAT
FC-i07
CM
START
- 4
FC-105
cbd
STOP '
KEY
Q-M?
u-r-i
START
RELAY
LI
I
REPEA1
-4
START
STOP |^
1,2 -"1 p STOP
-4
MAGNET
FC-106
OH
C-7-2
■-U
C-7-3
REPEAT READ
RELAY RELAY
, ^"7 STOP
C-8-IJ s SWITCH"
r-l
STOP
RELAY
Figure 20
These contacts will be considered in connection with the computing circuits of which they form a part.
The timing diagram, Fig. 19, together with the foregoing description should make clear the repetitive
operation of the circuits shown in Figs. 17 and 18 insofar as continuous operation of the calculator
is concerned.
Figure 20 and the diagram, Fig. 21, show the start and stop circuits and their timing. The de-
pression of the start key completes the circuit through FC-103 to pick up the start relay. The repeat
relay, one point of which is shunted across the start key, is controlled by the sequence relay, C -7. This
is picked up by the continue operations code, Miscellaneous 7. The transfer of the contacts of the start
relay closes the circuit, controlled by FC-105, to the read relay and the clutch magnet. This circuit
contains two normally closed contacts of the stop relay. The stop relay is picked up if, and only if, the
stop key is depressed and one of two circuits completed. The first of these is completed by FC-106
and relay contacts governed by the code Miscellaneous 87, while the second is governed by the code
57
ELECTRICAL CIRCUITS
ONE CYCLE
START RELAY FC- 103, 108
READ RELAY FC-105
SEQUENCE RELAY C-7 FC-101,102
SEQUENCE RELAY C-8 FC-101,102
REPEAT RELAY FC-107
STOP RELAY FC-106
Figure 21
Miscellaneous 7 in combination with the "7 stop switch". The stop relay is held up through one of its own
contacts and the stop key. The emergency stop switch is located on the sequence mechanism, (Plate VI).
The 87 stop and the 7 stop have decidedly different purposes. The 87 stop maybe so coded in a control
tape that if the stop key is depressed the machine will stop at a preassigned point in the computation.
On the other hand, the 7 stop switch together with the stop key will interrupt the operation of the
machine after reading any line of coding containing a Miscellaneous 7. This makes it possible to stop
the calculator at the end of any functional operation without interfering with the computation provided
that no operations have been interposed. Further discussion of the codes 87 and 7 is contained in
Chapter IV.
The relays, relay points and cam controlled contacts in Figs. 17, 18 and 20 have been indicated
and numbered as in the calculator itself. For simplicity, one relay, the start interlock relay, has been
omitted from these circuits. In the event that the start key is held down too long, the start interlock
relay prevents the calculator from receiving more than one starting impulse. The circuits of this relay
together with all of the automatic continue operation circuits which may energize the start relay are
given in Appendix II.
Unlike the main sequence control, the operations dictated by the subsidiary sequence control
are not subject to permutation. Consisting of relay networks and counters, the twenty subsidiary
controls at present wired in the calculator direct fixed series of operations. These are largely
58
ELECTRICAL CIRCUITS
r . _^___jl-_: *~ *U« ~~„+«,0 rvf fha fun/>Hnnal units HnweVer.
concerned witn tne sequences 01 operations ut;uee>»a.i-y tu mc v,umiui ^ w.v. iu.,v« u — - — — .
it is possible to construct a subsidiary sequence control for any given purpose. For example, the
evaluation of a definite integral may be reduced to the computation of values of the integrand for equi-
distant values of the argument by a short control tape, which also directs a subsidiary sequence control
wired to apply a general quadrature formula. In this instance, the coding necessary to the evaluation
of definite integrals is greatly reduced. Such specialized subsidiary sequence controls are added to
the calculator from time to time as may be desired. These differ only in the sense that some control
a greater number of operations and in that their control extends over a longer period of time. Unfor-
tunately, space will not permit the description of all of the sequence controls in the calculator. The
fa,.* frhofr +hr«:p (./."t-ninniT miii+iniifoHnn and division are not onlv the most simple, but also the more
basic in computation, dictates their choice for detailed discussion.
Before entering upon this subject, however, it will be necessary to discuss the use of counters
and their drive. Referring to Fig. 22, A is a line shaft extending nearly the full length of the calculator
and driven by the four horsepower motor, B. This shaft is contained in the shaft housing shown near
the base of the machine in Plates II,IIIandXII. The main sequence mechanism and the three interpo-
lator mechanisms are supplied with mechanical power by roller chain and sprocket drives, C and D,
MECHANICAL DRIVE SYSTEM
f^
rr 1 1 i
Figure 22
59
ELECTRICAL CIRCUITS
respectively. The spiral gears, E, connect the main drive shaft to the vertical shafts, F. These in
turn are connected to the horizontal shafts, G, through smaller spiral gears, H. On the shaft, G, are
mounted twelve or fewer gear wheels, J of Fig. 22, E of Plate XVII, each of which supplies mechanical
power to a single counter wheel by engaging with the gear shown in the partially assembled counter,
A of Plate XVII. Since the sequence and interpolator mechanisms and counter wheels are all driven
by a single gear-connected mechanical system, it is clear that all mechanical parts of the machine
revolve in synchronism with each other.
Each counter wheel is an electro-mechanical assembly consisting of the following major com-
ponents shown in Plate XVII: (1) a commutator mounted in a molded plastic part, B and J, commonly
called a "molding", having a half slip ring and ten segmental contacts numbered through 9; (2) a
pair of stranded wire brushes, C and F, which rotate to connect one of the contact segments with the
commutator half slip ring; (3) a magnetically controlled clutch, D, which engages to connect the con-
tinuously rotating gear, A, with the sleeve on which the rotating brushes are mounted; (4) a tenls carry
contact which operates in conjunction with an external relay circuit to provide carry to the counter
wheel in the next higher columnar position when the counter wheel under consideration passes through
ten; (5) a nine's carry contact which also operates in conjunction with an external relay circuit to
provide carry to the next higher counter wheel when the wheel under consideration stands on nine and
the next lower wheel has passed through ten; (6) and finally, a socket, G and K, by which the counter
assembly may be jack- connected to the calculator wiring.
The ten segments of the commutator are usually called the number "spots". The time interval
necessary for the brush to traverse the distance between two successive spots is one -sixteenth of a
cycle, the number spots being so spaced in the commutator as to minimize the ratio of the mechanical
backlash to the distance traversed between spots. In order to read, say, a seven into a counter, the
counter magnet is picked up at "seven time", thus engaging the clutch. The brushes are spun past
six spots and the clutch is mechanically disengaged or knocked off at "zero time". Obviously, nine
equally timed and equally spaced impulses must be provided to pick up the counter magnets in order
to read in the nine digits and all counters must be knocked off at zero time, (Fig. 23).
The number impulses are supplied by cam controlled contacts. A cam and its follower are
60
ELECTRICAL CIRCUITS
shown at the lower right in Plate XVI, and the position in which the cams are uiouiueu is Snown in
Fig. 22, K. The duration of contact controlled by a cam may be varied by adding or subtracting rollers
in the twenty possible sockets in a cam wheel. Several types of followers are used, with variations'
in the sharpness of the make and break of the contacts they control.
For purposes of cam timing, the fundamental cycle of the calculator, 300 milliseconds, is sub-
divided into sixteen equal parts commonly referred to as "points". These are numbered:
11 12 13 14 15 16
I I I I
i i i i
r»ne>
r«vr»l
p —
1 fi nnints
■>
The first nine subdivisions contain the number impulses. The so-called "seven impulse", for example,
is delivered by a cam contact making at seven time and breaking half way between seven and six time,
commonly called seven and one-half time. The points zero through sixteen are available to supply carry
and other control impulses. A timing diagram of the number and carry impulses is given in Fig. 23.
As stated in Chapter II, the transfer of a quantity to a reset counter and the process of addition
are one and the same. For instance, a counter stands at zero; a seven impulse picks up the counter
magnet at seven time; the counter wheel rotates through six positions, is mechanically knocked off
at zero time and comes to rest standing on the seven spot. On the other hand, if a counter stands at
9 8 7 6 5 4 3 2 I II 12 13 14 15 16
9 IMPULSE ■
8 IMPULSE
-» in ni ii op
6 IMPULSE
5 IMPULSE
4 IMPULSE
3 IMPULSE
2 IMPULSE
I IMPULSE
MECHANICAL KNOCK OFF
CARRY IMPULSE
MECHANICAL KNOCK OFF
CARRY CONTACT KNOCK OFF
Figure 23
61
ELECTRICAL CIRCUITS
five, a seven impulse picks up the counter magnet at seven time; the counter wheel rotates through
six positions, is mechanically knocked off at zero time and comes to rest standing on the two spot,
having passed through zero.
As the counter wheel turns, the carry cam, (Fig. 24 and F of Plate XVII), also turns. When the
rotating brush touches the nine spot, the follower of the carry cam is dropped and the nine's carry-
contact is made, (B of Fig. 24). As the counter wheel passes nine and approaches the zero spot, the
follower is raised and the ten's carry contact is made, (C of Fig. 24). The ten's carry contact once
made is maintained, (D of Fig. 24), until a mechanical knock off returns the carry contact to neutral
position, (A of Fig. 24), at fourteen and one-half time. Prior to this, the counter magnet, as shown in
Fig. 23, is again picked up at twelve time by the carry impulse if the carry relay circuits are closed
and if the ten's carry contact of the next lower counter is made. The counter magnet is also picked up
at twelve time by the carry impulse if the carry relay circuits are closed and if the nine's carry con-
tacts of the succeeding lower counters receive a carry impulse due to a still lower ten's carry. The
counter wheel moves one position for the carry and is again mechanically knocked off at thirteen time.
Figure 24
62
ELECTRICAL CIRCUITS
13
12
4
i
ii
iO
3
8
€
K
yj
•J
*
1,2,3 OUT- RELAY
4,5,6 IN -RELAY
7,8 CARRY RELAY
9 CARRY CONTROL RELAY
I0-24TH COL CARRY CONTACT -10
1 1 - 24TH COL. CARRY CONTACT" 9
12, 13 CARRY BOOSTERS
STORAGE COUNTER RELAYS
Figure 25
These operations may be clarified by considering the relay circuits associated with the storage
counters. The relays are shown in Plate X, and their usual numbering and position in Fig. 25. There
are thirteen individual relays providing the normal circuits for each counter. Some of these are
grouped to function as a single relay of more than twelve poles, this being the maximum number of
poles available in any single relay as such. Relays 1, 2 and 3 compose the out- relay, while 4, 5 and 6
compose the in-relay. Relays 7 and 8 are the carry relays, with 9 serving as the carry control relay.
Also part of the carry circuits are relays 12 and 13, the carry booster relays. The nine's and ten's
carry contacts, of the twenty-fourth column counter, control relays 11 and 10 respectively, these being
employed in the end around carry circuit.
The storage counter cams, SC-1 through -9, control the number impulses for reading out either
from a switch or from a storage counter. Figure 26 shows the circuits for a read-out. The out-relay
is energized by a circuit through the sequence relay cascade contacts as previously discussed. Begin-
ning at the positive terminal of the generator, the read-out circuit of a counter is completed to the
buss through the reset and invert relays, via the brushes connecting the number spots to the half slip
ring and thence through the out-relay. The read-out circuit of a switch is exactly similar except that
the commutator of the counter is replaced by the manually preset switch contacts. The" wiring by
which the energized invert and reset relays provide complements on nine and ten respectively is also
shown in Fig. 26.
In order to read into a counter, a circuit is completed through the in-relay connecting the buss
to the counter magnets and to the negative terminal of the generator. If a quantity is standing in the
63
ELECTRICAL CIRCUITS
1-c;
SC-I
tr^-
SO -2
tT^
SC-3
cr^
SC-4
SC-5
H
tJ^^i
SC-6
H
tr^
SC-7
SC-8
cr^-
SC-9
^
RESET
RELAY
°-L_
<> "T_
^T_
■°-t
P
^
°-L.
*-L-
<UT*
"1
INVERT
RELAY
OUT
RELAY
Figure 26
I2| 2-1? 1-12?
13) (12
BUSS
o
counter at the time of read- in so that addition must be performed, the carry circuits are utilized. As
shown in Fig. 27, the carry control relay, 9, is picked up by an impulse, controlled by SC-13, at two
time. The first point of this relay, through SC-12, then controls the pick up of the carry relays, 7 and
64
ELECTRICAL CIRCUITS
SC-12
,3) BUSS 02
IN- RELAY
r*l5-l2 rls-i
CARRY CONTACTS
SC-IO
-j-<^J J-v^y
H 4-12 rl 4_|
m:
13-3 13-2
*— -i i
k'k°i " £
}
8-12
r
COL. 24
n
r
.-'
t
COL. 13
T.
10 9
fl
&
r
7-12
COL. 12
» » •
SC-13
SC-14
WO
RESET
10
t
12-312-
■4
.'■■
r
COL. I
-4"
X 1
1 COL. I i 12 i
E JE P
/ STORAGE COUNTER MAGNETS AND RELAYS
Figure 27
8,at eieven time, rne secona point ux me t*ny wnuui iciaji a.*^ ~v* ^- ^w^w^w* ^-. ^w up t"i-j«-
of relays 11 and 10. These circuits are completed through the nine's and ten's carry contacts, re-
spectively, of the counter in the twenty-fourth columnar position. The carry circuits are closed on
all read-ins except resets, when the carry control relay is not picked up due to the opening of the nor-
mally closed contacts of the reset relay. The tenth point of this relay is in the pick up circuit of the
carry control relay.
If a counter, other than the twenty-fourth, has passed through ten and its ten's carry contact
has been made, the carry impulse, at twelve time, through SC-10 and the appropriate carry relay
point, will energize the magnet of the counter in the next higher columnar position. If the twenty-
ELECTRICAL CIRCUITS
65
SC-15
on
FC-IOO
t.
C-4-
SEQUENCE
RELAYS
CASCADE
CONTACTS
CODE MISC. 2
C-3-1
C-2-1
OUT
RELAY
Qr
'1
C3J
SEO.-I1-1
SC-18
i-2
n
24TH COLUMN
CARRY CONTACT
C-l-2
SEQUENCE -II
t
3-3
OUT
RELAY
£
INVERT
RELAY
Figure 28
fourth column counter carry contact stands at ten, relay 10 will have been energized at eleven time.
Then the carry impulse at twelve time controlled by SC-10 will travel through the first point of the
carry relay, 7, and pick up the magnet of the first column counter for an end around carry. Careful
study of Fig. 27 will make clear the operation of the circuits when several successive counters stand
on nine and a carry impulse is provided by the next lower counter.
The circuits for switches and storage counters including the circuits for all of the specialized
storage counters are given in Appendix HI. Further, the relay list, Appendix VI, includes all of the
normal and special storage counter relays together with specific functions of each of the relay points.
Among others in Appendix in will be found the circuits by means of which it is possible to read
positive and negative absolute magnitudes out of any storage counter. The first of these circuits finds
66
ELECTRICAL CIRCUITS
MUL! I^LIUAIMU " UlVISUrr U~£J
MULTIPLICAND- DIVISOR (3-6)
MULTIPLICAND- DIVISOR (4-8)
MULTIPLICAND- DIVISOR (7)
MULTIPLICAND - DIVISOR (5)
MULTIPLICAND- DIVISOR (9)
DIVIDEND
PRODUCT- QUOTIENT
CYCLE
Q-SHIFT SEQ.
MULTIPLIER
INTERMEDIATE
PLUG
BOARD
SWITCHES
RESET
PUSH
BUTTONS
BOARD
Figure 29
application in connection with the "intermediate" counter through which all quantities must be read in
passing into the multiply-divide unit. The operation of the positive absolute magnitude read-out circuit
is dependent upon the presence or absence of a nine in the twenty-fourth column. Upon read-out, the
presence of a nine brings about the pick up of the invert relay. Figure 28 illustrates the positive abso-
lnfp ■»>o'./4_r«i 1 4- oc omnlntroH '« /»nnnoptinn«nth tho ctrifacro iriiintpT'C Tn th^S fioriirfs f-^i-l fnr oyamnlp
lUlC .B. COU Will* SA.G ^Ui^VJVW AAA W^AAAAW\rffc-A*_«AA WiA-AA MXW. fcJI.WA.fcA.^jW WW <M*vU A w . a.** I., t «. k_, a. a £> »* A. w , W a. A. , J. w J. W A*AW- AAa£/a.1^ ,
refers to the first point of the fourth cascade relay in the C group. The particular C relays shown
are those necessary to the pick up of the sequence relay 11 called for by the code Miscellaneous 2;
c.f.,pagel6. The second branch of the circuit in Fig. 28 shows the pickup at thirteen time of storage
counter relay 11. This circuit is completed through 3-1, the first point on the third relay composing
the storage counter out- relay- and through the nine's carry contact of the twenty-fourth column counter.
The third branch circuit at fourteen time picks up the invert relay through the second point of storage
counter relay 11 and through the third point of the third relay composing the out-relay. The use of the
positive absolute magnitude read-out circuit has been explained here because the application of such
67
ELECTRICAL CIRCUITS
a circuit in multiplication and division will reduce the problem to one dealing with positive absolute
magnitudes only during these operations .
The counters in the multiply-divide unit and the functional units are not the simple single mold-
ing counters that compose the storage registers. The functional counters are equipped with several
commutators, each set in a separate molding, and have special wiring which enables these counters
to perform operations other than simple addition. The operations of adding into and resetting of the
multiple molding counters are, however, the same as in the case of the storage counters. The counters
of the multiply-divide unit maybe seen in Plate XI and are arranged as shown in Fig. 29. These
counterswill require individual description. For this purpose, a calculator consisting of six columns,
the sixth column being reserved for the algebraic sign, will be assumed. This miniature calculator
may perform all of the operations of the calculator itself. The correspondences given in the table
below will be valid under this assumption.
Register
Calculator
Column
Miniature Machine
Column
Switch
24
23
22-1
6
5
4-1
Storage Counter
24
23
22-1
6
5
4-1
Intermediate Counter
24
23-1
6
5-1
MC-DR Counters
24
23-1
6
5-1
MP Counter
23-1
5-1
PQ Counter
47
46-1
11
10-1
DD Counter
45-1
9-1
Q-Shift Counter
2-1
1
Sequence Counter
1
1
Cycle Counter
1
1
68
ELECTRICAL CIRCUITS
As previously mentioned, the most frequently used of the multipiy-divide counters is the inter-
mediate counter. The multiplicand (MC), divisor (DR), multiplier (MP) and dividend (DD) all pass
through this counter as they enter the multipiy-divide unit. All these quantities are read into the
intermediate counter just as they stood in the storage counter from which they were selected. All
four values are read out of intermediate to the appropriate counters as positive absolute magnitudes.
The MC and MP are transferred without being shifted, but the DR and DD are read out from the inter-
mediate counter so shifted that their first significant digits appear in the twenty-third and forty-fifth
columns of the DR and DD counters respectively.
The intermediate counter has twenty-four columns. The twenty-fourth column is a four com-
mutator, usually caned "lour molding", counter, xne ursi mo.unng is usee lor ordinary reav«=uuis aiui
resets. The second molding is used to determine whether it is necessary to sense through zeros or
through nines to obtain the amount of shift necessary in reading DR and DD to their respective counters.
The third molding, if the twenty-fourth column stands at nine, forms a part of the pick up circuit of
the relays controlling the entry of a nine into the forty-seventh, or sign counter, of the product-quotient
counter (PQ). The fourth molding, if the twenty-fourth column stands at nine, forms a part of the pick
up circuits of the intermediate invert relay which delivers the positive absolute value of MC, DR, MP
or DD if these quantities were negative when they entered the multipiy-divide unit. The remaining
twenty-three columns of the intermediate counter are three molding counters. The first moldings are
used for ordinary read-outs and resets. The second and third moldings are used when sensing through
zeros and nines respectively to determine the amount of DR or DD shift.
The nine integer multiples of the MC and DR are built up in the multiplicand-divisor counters
thxr>-T\D\ in fha tifci- fnni. nirnloo nt mulKnli poHnn onH rfitricir»n Tocrwaot'i'iTolxr Siv pniintprs stftriiwr th«»
V iu^ ^» V) ... w»~ »»*^» »w* ~,«*~~ ~» — r -—j. ,, . ,
(1-2), (3-6), (4-8), (5), (7) and (9) multiples, are used for this purpose. Of these, the first three are
equipped with "doubling" read-outs; i.e., they have extra moldings so wired that they may readout
either the number upon which they stand or twice that number. The wiring diagram of a doubling
counter is shown in Fig. 30. The number impulses are provided as usual by cam controlled contacts.
In the counter shown, the read-out may be through one of four relays; reset, build-up, times one or
times two. As shown, the doubling counter requires four moldings. The first molding is used for
69
ELECTRICAL CIRCUITS
ordinary read-outs and resets. The second molding is used for the doubling read-out when there is
no carry from the next lower column. The third molding is used for the doubling read-out when there
is carry from the next lower column. The fourth molding controls the doubling read-out of the counter
in the next higher columnar position, selecting its second or third molding according as there is not
or is carry from the counter under consideration. All of the MC-DR counters have twenty-four columns
except MC-DR (1-2), which has twenty-three, and all are equipped with normal carry circuits but no
end around carry. MC-DR (5), (7) and (9) are composed of single molding counters exactly similar to
those used in the storage registers.
It is interesting to note that two and five are the only integer multiples which may be obtained
from a static reading circuit without using an undue amount of equipment. In the case of the two multi-
ple, the only carry number is unity and hence a carry from the nth column to the (n + l)st cannot
affect a column of still higher order. Therefore, the circuits of a doubling read-out must pass through
not more than two counter columns. A similar situation obtains in connection with the five multiple
as may readily be seen. Since a quintupling counter is not used in the calculator, no further details
of such circuits will be given here.
The MP counter consists of twenty-three double molding counter wheels. The first molding of
each is used for resets. The second selects the proper multiples of MC to be read out of the MC-DR
counters .
The dividend counter has forty-five single molding columns. During multiplication, the multiples
selected by the even columns of the multiplier are added into DD in the proper columnar position.
Thus, if the digits in MP are 25137, then 3 x (MC) and 5 x (MC) are read into DD in the following
positions.
DD counter column
987654321
3x(MC)-
■5x(MCH*
The odd multiples of MC are cared for in the PQ counter which will be described later.
70
MC-DR DOUBLING
dcah - m IT
>-r-
NUMBER
SPOTS
O
5 O
o
6 O
2 O
1
3 O
8 O
4 O
9 O
92-2-24
O
i
I
I
o
u
I
?
I
I
ELECTRICAL CIRCUITS
^ TO BUILD UP RELAY
TO RESET RELAY
9
— O
-O
*— o
*— o
92-2-23
6
— O
fc— O
4
A
Q
TO TIMES
i
— O
u-L
I
I
1
1
►— O
•— O
o
o — *-
92-2-22
A
J_^
•— o
i— o
COLUMN 24
ONE RELAY
TO TIMES TWO RELAY
l
COLUMN 23
Figure 30 A
! <?
I
A
4
I
if
1
1
n
t-JU
I
1
I
COLUMN 22
M
W
71
ELECTRICAL CIRCUITS
M
TO BUILD UP RELAY
<p — i-
92-1-3
t^
W
L U U
1
1
1
— o
TO RESET RELAY
92-1-2
©
TO TIMES
i
1
6
©
©
l-l
* o
COLUMN 3
6
ONE RELAY
TO TIMES TWO RELAY
COLUMN 2
Figure 30 B
NUMBER
IMPULSES
FROM
READ OUT
CAMS
92-3- 1 THRU 4
1
1
92-3 -5 THRU 8
6
© ©
COLUMN I
72
ELECTRICAL CIRCUITS
tv..j*.~ Ai,*inir*~ tUa cuoAaecitro mnlHnloc nt T\Vt arp siihtT>3 r>te»d from the dividend in the DD
counter. Since these subtractions terminate at least one column to the right with each successive
operation, end around carry is replaced by the addition of an elusive one in the lowest order column
of each subtrahend.
The product-quotient counter has forty- seven columns. The forty- seventh column of PQ, some-
times called the sign counter, has two moldings. The first of these is used for resets. The second,
if the counter stands at nine, forms a part of the circuits picking up the DD-PQ invert relay, in order
to read out the negative product or quotient. The sign counter is the only one in the machine which
cannot be reset by button. If the machine is stopped before a multiplication or division is terminated,
care must be taken to see that this counter is manually reset before continuing operation. This must
be accomplished by manipulation of the armature of the counter magnet.
During multiplication, the multiples selected by the odd columns of the multiplier are added into
PQ in the proper columnar position. Thus, if the digits in MP are 25137, then 7 x (MC), (MC) and
2 x (MC) are read into PQ in the following positions.
PQ counter column
1110 98765432i
7 x (MC)-*
— (MC) "
2 x (MC)-
At the end of the multiplying operation, the multiples previously added into DD are transferred to PQ
and the final product read out from this counter. The device of adding the odd and even multiples of
MC into the PQ and DD counters, respectively, doubles the speed of multiplication because two multi-
ples may be added in each machine cycle.
The PQ counter in the case of division receives the digits of the quotient which are read in suc-
cessively, starting at the forty-sixth column.
The quotient shift counter (QS), as mentioned in Chapter II, is used to calculate the number of
columns the quotient must be shifted to the right upon reading out to the buss in order to conform with
73
ELECTRICAL CIRCUITS
the operating decimal position. This counter has two columns. The first column is a four molding
counter. Of these four moldings, the first is used for reset. The second, third and fourth are used
to read out quotient shifts amounting to zero through nine columns, ten through nineteen columns and
twenty through twenty-two columns, respectively. The second column of the QS counter has two mold-
ings . The first molding is again used for reset and the second to read out the tens digit of the amount
of shift in conjunction with the proper molding of the first column. The quantity standing in the QS
counter is not read out in the ordinary manner but rather the combination of number spots in the two
columns form a part of the pick up circuit required to select the appropriate section of the Q-shift
relay. During each dividing operation the QS counter receives four quantities. These are: (1) the
complement on nine of the amount of the DR shift left when reading from the intermediate counter to
the MC-DR counters; (2) the amount standing in the divide switch which is equal to 22 - n where the
operating decimal point lies between columns n and n + 1; (3) an elusive one in the first column; (4) the
amount of the DD shift left when reading from the intermediate counter to the DD counter. The total
standing in the Q-shift counter must always be positive, as no provision is made for shifting the
quotient to the left because quantities so shifted would be above the capacity of the calculator under
the assumed operating decimal position. The shift is counted to the right considering the forty-sixth
column of PQ as corresponding to the twenty-third column of the buss.
All of the multiply-divide counters so far described are controlled by a subsidiary sequencing
circuit which includes two special counters. The first of these is the sequence counter which has one
four molding counter wheel. When the first line of multiply or divide coding has been read, this counter
is stepped forward one position. It continues to step once each cycle during the build-up of the inte-
ger multiples of MC-DR, for the resets of the intermediate counter and finally for the read-out of the
product or quotient. This counter also has the function of signalling the main sequence mechanism to
read the line of coding supplying the multiplier or dividend and the line of coding delivering the product
or quotient. The first molding of the sequence counter is used for resetting. The functions of the re-
maining three moldings are best presented in a table which lists the relays whose pick up circuits are
governed by each position of the sequence counter. The table includes the relays used both in multi-
plication and division.
74
ELECTRICAL CIRCUITS
Seq.Ctr.
Second Molding
-LllirU JLYlUlUlllg
1
Intermediate In
Not used
DD-PQ Reset
2
Shift Pick Up
MC-DR In
Q-Shift Invert
Intermediate
Invert Control
3
First Build-Up
First and Second
Build-Up
Intermediate
Reset
4
Intermediate In
First and Second
Build-Up
Second Build-Up
Add-22
5
Shift Pick Up
MP-In
DD-In
Intermediate
Invert Control
N rt t used
Not used
Intermediate
Reset
7
Sequence Ctr.
Reset
MC-DR Reset
Product Out
8
Not used
9
Not used
The impulse which steps the sequence counter is not derived from the number impulse cam con-
*.*.-.«■-* mvs- ;-..„.. i__ ;,- — -__ii~J «+ ~~-~ +i>vi« *«» n "■"" nnntrnl 1 orl nnntunt f?C!-10. 3nH nORltinnfi the
taClS. J.I11S lIlipuiSc 1£> OUppJLlcU at. iciu ii"Iv. ujr **■ <-"■»" ^«^»* ~*~~„ „ _!., --, r
sequence counter fifteen points earlier than all other multiply-divide counters in order to give the
associated relay circuits ample time to operate before numbers are transferred.
The second special counter employed by the multiply-divide unit is the cycle counter, which
consists of one five molding counter of which the fifth molding is used for resetting. The first four
moldings of the cycle counter control the multiplying and dividing operations between sequence counter
positions six ana seven, i/unng mun.ipn.ca.iiuu uic ^jr^xc wuui« o^^ unv,w ^«.v,i» vj^ «***~ ~*v.w~ * v ~*
moldings determine the columnar positions in DDandPQ to which the multiples of MC are read. Dur-
ing division the cycle counter steps once each subtracting cycle, controlling the columnar positions in
DD from which the multiples of DR are subtracted.
The complete circuits for multiplication are given in Appendix IV, and for division in Appendix
V. These appendices also include timing diagrams which give the positions of relay and counter mag-
75
ELECTRICAL CIRCUITS
nets as picked up and held by impulses through the cam controlled contacts . The relays used in multi-
plication and division, including the functions of each wired point, are listed in Appendix VI. Each
cam, with the time of make and break of its contact and its function, appears in Appendix VII. The
multiply-divide fuses are classified in two ways in Appendix VHI; first, listing the relays and the fuse
to which each is connected, and second, listing the fuses and the relays which they serve. Figure 31
shows, cycle by cycle, the transfers of quantities from counter to counter in the multiply-divide unit
during the multiplication 0.3461 x 2.5137 = 0.8699. The operation is carried out on the miniature six-
column calculator previously mentioned.
Cycle
The sequence mechanism reads the first line of multiply coding (A, 761, blank). The sequence counter
advances to one.
Cycle 1
The MC is read from storage counter A via the buss to the intermediate counter. The intermediate
carry circuits, including end around carry, are energized. The DD, PQ and QS counters are reset.
The sequence counter advances to two.
Cycle 2
The positive absolute value of MC is read into MC-DR (1-2), (3-6), (5), (7) and (9) within the multiply
unit, (Fig. 32). The sequence counter advances to three.
Cycle 3
If a nine stood in the twenty-fourth column of the intermediate counter (MC ^ - 0), a nine is read into
the forty-seventh column of PQ. The intermediate -counter resets. The first build-up takes place;
i .e ., the first step is taken in building up the nine integer multiples of MC . Twice the MC is read from
the doubling moldings of MC-DR (1-2) to MC-DR (3-6), (4-8), (5) and (9) within the multiply unit,
(Fig. 32). The sequence counter advances to four. The sequence mechanism reads the second line of
multiply coding (B, blank, blank).
Cycle 4
The MP is read from storage counter B via the buss to the intermediate counter. The complete inter-
mediate carry circuits are energized. The second build-up takes place, completing the nine integer
76
ELECTRICAL CIRCUITS
1
Cjc
No.
Storage
Counter
Seq
Ctr
Intermediate
Counter
MC-DR (I-*)
Counter
MU-DJK. (3-6)
Counter
MC-DR (4-8)
Counter
mj—ua. \jt
Counter
3 4 6 1
MC
1
1
1
IK to Int
1
1
2
3 4 6 1
3 4 6 1
2
2
1
3
MC to MC-DR
(1-2), (3-6)
(5), (7), (9)
3 4 6 1
3 4 6 1
3 4 6 1
3 4 6 1
3461
3 4 6 1
3
2 5 13 7
MP
3
3 4 6 1
7 6 4 9
2 times MC
to MC-DR
3 4 6 1
6 9 2 2
10 3 8 3
6 9 2 2
6 9 2 2
3 4 6 1
6 9 2 2
10 3 8 3
4
MP to Int
4
1
5
2 5 13 7
2 5 13 7
2 times MC
to MC-DR
(4-8), (5)
6 times MC
to MC-DR
(7), (9)
6 9 2 2
6 9 2 2
13 8 4 4
10 3 8 3
6 9 2 2
17 3 5
5
5
1
6
to MP
6
2 5 13 7
8 5 973
to DD
7
to FQ
to DD
8
to FQ
9
10
L
7
7 6 4 9
e\ r\ <\ r\ f\
n i n •* ft ?
9 7 2 7
a r\ n a a A
n i ^ ft t. l
9 7 2 6 6
a a a A A A
o i 7 i n 5 1
9 7 3 5
A A A A A A
11
8 6 9 9
o b & 6 9 9
p
7
3
IT
Figure 31 A
ELECTRICAL CIRCUITS
77
MC-DR (7)
Counter
MC-DR (9)
Counter
MP
Counter
Cyc
Ctr
DD
Counter
PQ
Counter
Cyc
No.
329763180
02964153287
329763180
78134792
000000000
02964153287
8146957823
00000000000
1
3 4 6 1
3 4 6 1
3 46 1
3 4 6 1
2
3 4 6 1
6 9 2 2
10 3 8 3
"o*
3
3 4 6 1
2 7 6 6
24227
10 3 8 3
2 7 6 6
3 114 9
4
2 5 13 7
2 5 13 7
1
1
5
to PQ
1
1
2
000000000
1 3 8 3
000103830
00000000000
2 4 2 2 7
00000024227
6
2
1
3
000103830
17 3 5
00000024227
3 4 6 1
7
017408830
00000370327
3
1
4
00000370327
6 9 2 2
8
00069590327
4
1
5
! to PQ
0006959 3 27
8 8 3
00069599157
9
2 4 2 2 7
8 6 8 8 3
3 114 9
7 9 961
5
A.
to PQ i
00069599157
17 4
10
00086999157
to Storage
11
Figure 31 B
78
ELECTRICAL CIRCUITS
INTERMEDIATE
r.Yr.i F 3
CYCLE 4
MC-DR(l-2)
MC-DR(3-6)
MC- DR (5)
MC-DR (7)
MC-DR(l-2)
MC-DR (3-6)
MC-DR (4-8)
MC-DR (5)
MC-DR (4-8)
MC- DR(5)
{ ] MC- DR (7)
i V
I MC-DR (9) | | MC-DR (9) | ] MC-DR (9) |
Figure 32
multiples of MC-DR. Twice the MC is read from the doubling moldings of MC-DR (1-2) to MC-DR (4-8)
and (5). Six times MC is read from the doubling moldings of MC-DR (3-6) to MC-DR (7) and (9),
(Fig, 32), The sequence counter advances to five.
Cycle 5
The positive absolute value of MP is read to the MP counter from the intermediate counter. The
sequence counter advances to six. The cycle counter advances to one.
Cycle 6
K a nine stood in the twenty-fourth column of the intermediate counter (MP ^ - 0), a nine is read into
the forty- seventh column of PQ. There is no end around carry from column forty-seven to column one
of PQ. The eight spot of column forty-seven of PQ is jumpered to the zero spot. The algebraic sign
is, therefore, cared for in the following manner.
+ . + = + corresponds to + = 0,
+ . - = - corresponds to + 9 = 9,
- . + = - corresponds to 9 + = 9,
- . - = + corresponds to 9 + 9 -* 8 -•* 0.
79
ELECTRICAL CIRCUITS
If, at the end of multiplication, a nine stands in the forty-seventh column of PQ, the product is in-
verted as it is read out into the buss, since it stands in PQ as a positive absolute magnitude. The
intermediate counter resets and is ready for the next multiplying or dividing operation. Under control
of the cycle counter, the multiples corresponding to the digits in the first and second columns of MP
are added into PQ and DD respectively. The cycle counter is advanced to two.
The multiples of MC continue to be selected in pairs and added, while the shift circuits advance
the columns of entry into PQ and DD under control of the cycle counter. If both of a pair of digits of
MP, one in an odd and one in an even column, are zero, the next pair of multiples is immediately
properly shifted and added. If the entire MP is zero, cycle 6 is combined with cycle 9. If the MP is
not zero, but contains n non-zero digits in either the odd or even numbered columns, whichever is the
greater, then n - 1 cycles intervene between cycle 6 and cycle 9— 6 + n. Thus, in order to increase
the speed of multiplication, whenever possible the number having the fewer non-zero digits should be
used as the multiplier. If a multiplication is to be performed in which one factor is a constant, this
quantity should usually be used as the multiplier because the number of non-zero digits and their po-
sitions are known. This makes it possible to interpose a predetermined number of operations during
the multiplication. (See Chapter IV, Coding, Multiplication.)
Cycle 7 (4 + n)
A pair of multiples is added into PQ and DD. The cycle counter is advanced.
Cycle 8 (5 + n)
The last pair of multiples is added into PQ and DD. The cycle counter is advanced.
Cycle 9 (6 + n)
The first DD to PQ transfer takes place. The quantity standing in the lower half of DD is added into
the lower half of PQ. The cycle counter is advanced for the last time. If MP = 0, this cycle combines
with cycle 6.
Cycle 10 (7 + n)
The second DD to PQ transfer takes place. The quantity standing in the upper half of DD is added into
the upper half of PQ. The MC-DR,MP and cycle counters are reset in preparation for the next oper-
ation. If the multiplying operation is interrupted, these counters together with the intermediate,
80
ELECTRICAL CIRCUITS
sequence ana .hq sign counters musi ue mauuany rcaci uciuic wuuuui.i* & w^^vi^. -.. h
counter advances to seven. The sequence mechanism reads the last line of multiply coding (blank, C, 7).
Cycle 11 (8 + n)
The product is read out to storage counter C via the buss and the multiply plugging. (See Chapter V,
Plugging Instructions.) The product is inverted if a nine stands in the forty-seventh column of PQ.
The sequence counter and the forty-seventh column of PQ, the sign counter, are reset. The sequence
mechanism reads the next line of coding.
It may readily be seen from Fig. 31 that the rounding off error in multiplication is less than one
in the lowest order column read out; i.e„ if the operating decimal point lies, for example, between
„^v., 51ir c: 15 ar ,r| ig tha roundin- off error will be less than 1 x 10 .
Included in Appendix IV are the circuits of the low order read-out of PQ and of the normalizing
register, both described in Chapter II. The use of these circuits and their coding is considered in de-
tail under High Accuracy Computation and Normalizing Register in Chapter IV.
Division makes use of all of the functional counters used in multiplication except the MP counter.
This process does, however, make use of the QS counter, previously described on page 72. The pair
of dial switches just to the right of the sequence mechanism must be set to 22 - n where the operating
decimal point lies between columns n and n + 1 . Division also requires plugging to terminate the
operation after the desired number of comparisons have been made. This plugging and the coding
controlling it are considered under Division in Chapters IV and V.
Figure 33 shows the transfer, cycle by cycle, of the quantities in the multiply-divide unit during
division. Again the miniature six -column calculator is used for purposes of illustration. The division
of - 0,375 by + 0.213 to give - 1.760 is performed. The operating decimal point is considered to lie
between columns three and four, the divide switch being set at 4 - n = 4 - 3 = 1, since column four of
the miniature calculator corresponds to column twenty- two of the actual machine. The division is
considered to be plugged for five comparisons.
Cycle
The sequence mechanism reads the first line of divide coding (A, 76, blank). The sequence counter
advances to one.
81
ELECTRICAL CIRCUITS
Cycle 1
The DR is read from storage counter A via the buss to the intermediate counter. The intermediate
carry circuits, including end around carry, are energized. The DD, PQ and QS counters are reset.
The sequence counter advances to two.
Cycle 2
The positive absolute value of DR is read, without traversing the buss, to MC-DR (1-2), (3-6), (5), (7)
and (9) so shifted that its highest significant digit appears in the twenty-third column of MC-DR (1-2).
The complement on nine of the number of columns the DR is shifted left is read into the QS counter.
An elusive one is read into the first column of the QS counter. The sequence counter advances to
three.
Cycle 3
If a nine stood in the twenty-fourth column of the intermediate counter (DR £ - 0), a nine is read into
the forty-seventh column of PQ. The intermediate counter resets. The first build-up takes place.
Twice the DR is read from the doubling moldings of MC-DR (1-2) to MC-DR (3-6), (4-8), (5) and (9)
within the multiply-divide unit. The sequence counter advances to four. The sequence mechanism
reads the second line of divide coding (B, blank, blank).
Cycle 4
The DD is read from storage counter B via the buss to the intermediate counter. The complete inter-
mediate carry circuits are energized. The second build-up takes place, completing the nine integer
multiples of DR. Twice the DR is read from the doubling moldings of MC-DR (1-2) to MC-DR (4-8)
and (5). Six times DR is read from the doubling moldings of MC-DR (3-6) to MC-DR (7) and (9). The
quantity standing in the divide switch is read into the QS counter. The sequence counter advances to
five.
Cycle 5
The positive absolute value of DD is read into the DD counter so shifted that its highest significant
digit appears in the forty-fifth column of DD. The number of columns the DD is shifted left is read
into the QS counter, completing the computation of the number of columns the quotient must be shifted
to the right when it is read out. The sequence counter advances to six and the cycle counter to one.
82
ELECTRICAL CIRCUITS
Cyc
No.
— — — — . ,
Storage
Counter
Seq
Ctr
Intermediate
Counter
MC-DR (1-2)
Counter
im no f 1 „Ji^
Counter
lgJ_T)R (5)
Counter
2 13
DR
1
1
oooooo
oooooo
oooooo
1
DR to Int
1
1
2
2 13
2 13
2
2
1
3
DR to MC-DR
(1-2), (3-6)
(5), (7), (9)
2 13
2 13
oooooo
2 13
2 13
oooooo
2 13
2 13
9 9 9 6 2 4
DD
3
1
4
2 13
8 9 7
oooooo
2 times DE
to MC-DR
(3-6),(4-8)
2 13
4 2 6
6 3 9
oooooo
4 2 6
4 2 6
2 13
4 2 6" I
6 3 9 j
1
-
DD to Int
1
5
9 9 9 6 2 4
9 9 9 6 2 4
2 times DR
to MC-DR
(4-8), (5)
6 times DR
to MC-DR
(7), (9)
4 2 6
L 2 6
6 3 9 j
4 2 6
8 5 2
10 6 5 I
5
5
1
6
to DD
6
9 9 9 6 2 4
1114 8 6
to DR
Compare
to DR
Compare
to DR
Compare
to DR
Compare
oooooo
7
inverted
to DD
i
8
to DR
j Compare
to DR
Compare
to DR
Compare
to DR
Compare
" 9
10
to DR
Compare
to DR
Compare
to DR
Compare
to DR
Compare
11
i
i
I
6 times DR
inverted
I t-o DD
i
i 1
12
OU JJit ,
Compare
1 4- c no
Compare
1 to DR
Compare
1 to OR
Compare
13
to DR
Compare
to DR
Compare
to DR
Compare
to DR
Compare
14
6
1
7
inverted
to DD
15
9 9 8 2 3 9
9 9 8 2 3 9
7
JL
2 13
8 9 7
6 3 9
4 7 1
oooooo
8 5 2
2 5 8
oooooo
10 6 5
9 4 5
oooooo
Figure 31
J A
ELECTRICAL CIRCUITS
83
MC-DB (7)
Counter
HC-DR (9)
Counter
QS
Ctr
Cyc
Ctr
DD
Counter
PQ
Counter
Cyc
No.
2
16364967
88532075484
2
8
163649670
94746143
000000000
88532075484
22578 35626
00000000000
1
2 13
2 13
7
1
8
2
2 13
2 13
2 13
A 2 6
6 3 9
~6~
3
2 13
12 7 8
14 9 10
6 3 9
12 7 8
19 17
8
1
9
4
9
2
1
1
1
000000000
3 7 5
375000000
5
to DR
Compare
to DR
Compare
to DD
Compare
9
9
6
1
1
T
375000000
7 8 6 9 9
1
90000000000
1
7
91000000000
162000000
to DR
Compare
to DR
Compare
to DD
Compare
8
inverted
to DD
2
1
3
162000000
8 5 8 9 9
1
91000000000
7
9
91700000000
012900000
to DR
Compare
to DR
Compare
to DD
Compare
10
3
1
4
012900000
8 7 2 19 9
1
91700000000
6
11
91760000000
100120000
to DR
Compare
to DR
Compare
to DD
Compare
12
to DR
Compare
to DR
Compare
to DD
Compare
13
4
1
5
100120000
8 9 3 4 9 9
1
91760000000
5
14
91760500000
101013500
14 9 10
9 6 19
19 17
9 19 3
5
5
9
1 to Storage
15
Figure 33 B
84
ELECTRICAL CIRCUITS
Cycle 8
If a nine stood in the twenty-fourth column of the intermediate counter (DD < - 0), a nine is read into
the forty-seventh column of PQ, completing the determination of the algebraic sign of the quotient by
the same means as are used In multiplication. The intermediate counter resets and is ready for the
nest multiplying or dividing operation. The nine integer multiples of the divisor are read to the DR
compare relay and the dividend is read to the DD compare relay. A sensing circuit through the com-
pare relays selects the largest multiple of the divisor less than the dividend. If all multiples are
greater than DD, the cycle becomes a "no go" cycle and the comparison is made again, shifted one
column to the right, in the next succeeding cycle. Since all comparing operations are identical, the
.... -,-h^« ■=,-*" *v= <"„ s * M foH and described in connection with cycle 10.
comparing circuits ana meir ope^-awo.. -i Ji ~- *«»- ***-*
Cycle 7
The selected multiple of DR is subtracted from DD, with an elusive one added in the first column of
the subtrahend. The digit defining the multiple is entered in the PQ counter. The cycle counter Is
advanced.
Cycles 8 and 9
These two cycles of the example duplicate the compare and subtract operations described in cycles 8
and 7.
Cycle 10
This cycle duplicates the comparing operations performed in cycles 6 and 8. According to Fig. 33,
the quantity 012900000 now stands in the DD counter. Since, in the example, cycle 10 makes the third
comparison, thequantity 129000 is transferred to the DD compare relay. This transfer is accomplished
_ ~— ^ m . M ,h nnP column is shown in Fig. 34. In these and following circuits, certain relay
and hold points,not necessary to the discussion, have been omitted for the sake of brevityand clarity.
The complete circuits will be found in Appendix V.
The quantity 129000 is transferred to the DD compare relay by impulses derived from the cam
controlled contacts CC-1 through -9. By impulses derived from the same cam controlled contacts,
Fig. 34, each of the nine integer multiples of the divisor is read to the DR compare relay. The com-
pare relays are all provided with hold circuits, not shown in the figure, such that these relays once
85
ELECTRICAL CIRCUITS
OD COUNTER COLUMN 6
o-
k
p' p* *>* m (" (•
DR COMPARE RELAY COLUMN 6
Figure 34
86
ELECTRICAL CIRCUITS
CC-24
DD COMPARE
RELAY
COLUMN 6
DR COMPARE
RELAY
COLUMN 6
9-2 9-1 8-2
9 OVER^t^ 8 OVER
! 9 UNDER
jojo 7 0VERJOJO
I ] 8 UNDER | J 7
7-1 6-2
6 OVER <
UNDER
DD COMPARE
RELAY
COLUMN 6
DR COMPARE
RELAY
COLUMN 6
OVER -UNDER RELAY
Figure 35
picked up remain energized until twelve time. With the aid of the compare relays, DD is compared
with each of the nine integer multiples of DR at one and the same time. How this is accomplished will
be explained for the case of the sixth column of the miniature calculator. The integer standing in this
column of DD is one. The integers standing in the corresponding columns of the multiples of DR, one
through nine,are 0, 0, 0, 0, 1, 1, 1, 1, 1, respectively. At "one time" the DD compare relay is picked
up. At the same time, the DR compare relays associated with the five, six, seven, eight and nine
multiples are likewise picked up. As previously stated, all these relays are held until twelve time.
The DD and DR compare relays have contacts wired as shown in Fig. 35, known as the over-under
circuits. The over and under relays are picked up by impulses supplied by the cam controlled con-
tact, CC-24, which is timed one-quarter impulse later than each of the number impulses derived from
CC-1 through -9. Each over relay is picked up through a normally open point of a DR compare relay
87
ELECTRICAL CIRCUITS
and a corresponding normally closed contact of the DD compare relay. Similarly, each under relay
is picked up through a normally closed point of a DR compare relay and a corresponding normally
open contact of the DD compare relay. Three cases must now be distinguished. (1) If the digit of a
DR multiple is greater than the digit of DD,the DR compare relay corresponding to the given multiple
is picked up before the DD compare relay and a circuit is completed through the normally closed point
of the DD compare relay and the normally open point of the DR compare relay to pick up the over relay.
(2) If the digit of a DR multiple is less than the digit of DD, the DR compare relay corresponding to
the given multiple is picked up after the DD compare relay and a circuit is completed through the nor-
mally open point of the DD compare relay and the normally closed point of the DR compare relay to
pick up the under relay. This is true of the one, two, three and four multiples in the example under
consideration. (3) If the digit of a DR multiple is equal to the digit of DD, the DR and DD compare
relays are picked up simultaneously and no circuit is completed to pickup either an over or an under
relay. This situation occurs in the case of the five, six, seven, eight and nine multiples in the example.
All of the over-under relays, like the compare relays, are held until twelve time. Recalling that
Figs. 34 and 35 are drawn for one column only, it should now be clear that the miniature calculator
has six DD compare, fifty-four DR compare and ninety-nine over-under relays corresponding to
twenty-four DD compare, 216 DR compare and 423 over-under relays in the calculator itself.
The over-under relays of all columns have contacts connected to form nine identical circuits,
called Q control circuits, one of which is shown in Fig. 36. These circuits are supplied with an
+ CO- 37
L_ OVER
•*! RELAYS
UNDER
RELAYS
COL- 6 COL- 5 COL-4 COL- 3 COL- 2 COL-
Q- CONTROL -6
Figure 36
I-
88
ELECTRICAL CIRCUITS
imnnlsp at eleven time b^thecam controlled contact CC-37 Each circuit controls the "icku" of one of
the nine Q control relays. The operation of these circuits may be made clear by a discussion of the
relays associated with the two highest columns. Three cases must again be distinguished. (1) If the
digit of a DR multiple is greater than the digit of DD in the sixth column, Fig. 36, the normally closed
over relay contact of column six will be open. No circuit will be closed to pick up a Q control relay.
(2) If the digit of a DR multiple is less than the digit of DD in the sixth column, the over relay contact
remains closed, the under relay transfers its contact and the circuit is completed to energize a Q con-
trol relay. (3) If the digit of a DR multiple is equal to the digit of DD in the sixth column, neither the
over nor the under relay is picked up. In this case the operation of the circuit is controlled by the
over-under relays associated with the fifth column and so on c
In the particular case of the example under consideration, the sixth Q control relay is picked up
by the normally open under relay contact of column four, since the digits in columns six and five have
been found equal . The Q control relays once picked up are held until nine time .
The last step in the comparison cycle consists of the selection of the multiple of the divisor to
be subtracted from the DD counter in the next succeeding cycle. This is accomplished by the circuit
shown in Fig. 37 made up of contacts of the Q control relays of which there are nine, one for each
integer multiple. The Q control relays have, by the over-under relays, been divided into two classes:
those not picked up, corresponding to DR multiples greater than DD; those which are energized and
correspond to DR multiples less than DD. In Fig. 37, the cam controlled contact CC-31 at twelve and
Q CONTROL RELAYS
r£
r£
r£
r£
H H n rM
rK
TIMES RIGHT RELAY
Figure 37
89
ELECTRICAL CIRCUITS
one-half time delivers an impulse to pick up the appropriate part of the "times right" relay corre-
sponding to the positions of the contacts of the Q control relays. In the example, the nine, eight and
seven multiples are all greater than DD, while the six multiple is the largest multiple less than DD.
Hence, the impulse supplied by CC-31 passes through the normally closed Q control contacts nine,
eight and seven, and through the normally open contact, six, to the six times section of the times right
relay. In the next cycle this six times section of the times right relay serves as an out relay when
reading the selected six multiple to the DD counter for subtraction. The times right relay also
controls the entry of the digit defining the multiple into the PQ counter. The simple circuit for ac-
complishing this is given in Appendix V.
Cycle 11
This is a subtract cycle duplicating the subtracting operation of cycles 7 and 9. The appropriate digit
is entered into the PQ counter. The cycle counter is advanced.
Cycle 12
This is a compare cycle which yields a no go in the example.
Cycle 13
This is the fifth compare cycle. The place limitation plugging becomes operative to energize the relay
circuits terminating the division under discussion. If the calculator is plugged for n comparisons, a
minimum of n + 1 cycles and a maximum of 2n cycles will occur between the reading of the dividend
to the DD counter (cycle 5) and the read-out of the quotient (cycle 15).
Cycle 14
The last subtraction is made in the DD counter and the last digit of the quotient entered in the PQ
counter. The cycle and sequence counters are advanced for the last time. The sequence mechanism
reads the last line of divide coding (blank, C, 7).
Cycle 15
The quotient is read out to storage counter C via the buss and that part of the quotient-shift relay
selected by the quantity standing in the QS counter. The quotient is inverted if a nine stands in the
forty-seventh column of PQ. The MC-DR, sequence, cycle and sign (forty-seventh column of PQ)
counters are reset. The sequence mechanism reads the next line of coding.
90
ELECTRICAL CIRCUITS
It may be seen from Fig. 33 that the rounding off error in division is either less than one in ~.e
lowest order column read out, or less than one in the column in which the last comparison is made.
If the operating decimal point lies between columns 15 and 16 and division is plugged for n compari-
sons, the rounding off error is less than lxI0" 15 or Ix 10~ n , whichever is the greater.
The discussion of division completes the description of the fundamental computing circuits of
the calculator, those of addition, subtraction, multiplication and division. There remain to be dis-
cussed the functional units. These consist of subsidiary sequence circuits which control the multiply-
divide unit and certain special counters. These counters are mounted to the right of the multiply-
divide unit, Plate XI, and are arranged as shown in Fig. 38. Among the special counters are the
-. its i_ i. 4. /T ts\\ *u^ u«« w uh m r^un^T fi.nn\ the cYnnnpttti a l in -nut counter (EIQ) and
lOgelX'iUllXl IU-UUI UUUUI.CJL \xjL\Sf } urc lugdnuiui wtutwi. v -~w~/,— .~ — -* =~ -— - - ■>
the sine in-out counter (SIO). As described on pages 37 and 38, the LIO and SIO counters are available
for arithmetic operations in addition to their normal use in their respective units. The logarithm
sequence (LS), logarithm cycle (LC), exponential sequence (ES) and two sine sequence (SS and SSg)
counters are subsidiary sequence controls similar to the sequence and cycle counters of the multiply-
divide unit. In addition to the functional counters and the multiply-divide unit, these sequence counters
PRINT
I (1-12) |
PRINT
I (13-24)
PRINT
H (1-12)
PRINT
31 (13-24)
zi-z* |
INT. GK.
INTERPOLATION
LiO
(i-20)
ES
LC
LS
LOG (1-23)
EIO
(1-24)
ss 2
SS,
SIO (1-24)
LS 2
LS,
PS
PUNCH (1-24)
Figure 38
91
ELECTRICAL CIRCUITS
also control certain table relays. The wiring of a table relay (columns thirteen through twenty-four)
containing -t and reading directly into the buss is shown in Fig. 39. Such a relay is picked up through
the subsidiary sequence control and held through one of its own points during that part of a machine
cycle given over to the nine number impulses.
Since the computation of the logarithm, exponential and sine is accomplished by the multiply-
divide unit operating in conjunction with the functional counters and certain table relays, a complete
discussion of the electro-mechanical tables of these functions would further require only a description
of the functional sequence circuits . The theory of the methods employed together with the order in
which the operations are performed in the computation of the logarithm, exponential and sine was set
forth on pages 28 through 37 of Chapter II. The sequence circuits of the functional units are elaborate
extensions of the circuits already described under multiplication and division covering a great many
cycles. They would require a protracted discussion to set forth their operations cycle by cycle . Since
no new ideas of circuit design are introduced, the description would add but little to an understanding
of the basic principles of the calculator. Hence, the functional units will receive no further attention
here.
®
BUSS COLUMNS 24-13
(O) (5) (CO (O) (CO
TT RELAY
CC-I CC-2 CC-3
Ctr Or
CC-4 CC-5
CM Cp Cm Ct
CC-6 CC-7 CC-8 CC-9
NUMBER IMPULSE CAMS
Figure 39
92
ELECTRICAL CIRCUITS
The interpolator units make use of three special counters (Fig. 38), the interpolation, the in-
terpolation check and the 7L counters. All three of these function during tape positioning. As stated
in Chapter n, the interpolation counter receives the argument (and the highest order column of h) to
which the tape is to be positioned. The interpolation check counter also receives the argument, in
order to check the position of the tape when the interpolator mechanism has come to rest. The X^
counter counts the number of coefficients passed over in stepping the tape and signals for a one to be
added or subtracted from the interpolation counter for each argument passed over. Once the tape has
been positioned, relay networks together with the X* counter control the computation. The interpo-
lation sequence circuits again are of the same general type as those used in the functional units,
is further complicated by the necessity of reading numerical values from a tape. The reading of a
functional or value tape is similar to the reading of a sequence control tape, except that four lines of
holes, covering the same space as two lines of coding are read simultaneously, (Figs. 13 and 14).
Fig. 40 shows one column of the wiring employed for this purpose. The reading contacts are closed
in the distribution demanded by the punching in the tape, not shown in the figure. An impulse supplied
by FC-54 passes through the closed reading contacts to energize the value tape relays. These relays
are held through their own fourth points and FC-55, The value tape relays, like the sequence relays,
COLUMN N
READING CONTACTS
cfi eta
FC-54
VALUE TAPE RELAYS
FC-55
< '
Figure 40
93
ELECTRICAL CIRCUITS
form a cascade. The nine number impulses are read through a cascade (Fig. 41) for each column of
the tape to the corresponding column of the buss. Actually, Fig. 41 is drawn for the case of a value
tape rather than a functional tape and hence reads directly into the buss without passing through the
plugging and relays as required by the process of interpolation. (See Chapter V, Interpolators.)
In addition to the counters given over to the electro-mechanical tables of functions, Fig. 38 also
shows the print and punch registers employed in the recording of computed results . The punch regis-
ter has twenty-four double molding counters and is equipped with complete carry circuits including
end around carry. The first moldings are employed for resets and for ordinary read-outs, thus making
the punch register available for use as an additional storage counter. The second moldings are used
to deliver the quantity standing in the punch register to the punch itself. This is accomplished by means
BUSS COLUMN N
CC-4 CC-3
era era cij cN oi 01
2-2
CC-2 CC-9 CC-8
M
J;
CC-I
Cm el Ci]
CC-7' CC-6 CC-5
L±
NUMBER IMPULSE CAMS
Figure 41
94
ELECTRICAL CIRCUITS
uuLumn jLLUuiiwii
COL 24 COL 23 COL 22 COL 2 COL I
PUNCH COUNTER - SECOND MOLDINGS
Figure 42
PUNCH
MAGNETS
of the circuit shown in Fig. 42. An impulse through the column selection contact of the punch and
through the energized punch relay passes to the half slip ring of the twenty-fourth column of the punch
counter. From the half slip ring it travels via the brushes to the number spot, through another con-
tact of the punch relay to the punch magnets . The punch magnets control the punches which perforate
a standard tabulating machine card as shown in Fig. 43. The quantity e, the base of natural logarithms,
and a serial number have been entered in this card. The operation of the punch magnets also com-
pletes circuits which control the forward motion of the card to the next column and the movement of
the column selection contact to the next lower column of the punch counter. The operation is repeated
until the integer in column one has been punched. The card is then skipped out of the punch and stack-
ed. The punch relay is energized and the punching operation initiated by the code Miscellaneous 5.
The normally closed contacts of the punch relay, not shown in the diagram, complete the ordinary
read-out circuits of the punch counter.
95
ELECTRICAL CIRCUITS
looooooooooooolooooooolooooosooooooo
1 1 ill i ill 11111 mi ii 11111111111111 ii
2|222|222|2222 222|222 222 222 22 22 2 222 2
33 3 3 33 3333 3 333 3 3 33i3l3 31333333 333333
4444444444 414 4 4|4 4444444444444444444
5 5 5 5 5 5 5 5 5 5 5 5|5 5 5|5 5|5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
66 6 666666666 66666666 6166666666666666
771777 777777 7 7 77 7 7 77 77 7777 7777777777
8 888I8III8I8 888888 888 8888888 161 8 888 8
99999 9 9 99999913 999 9 39999 99 99 999 99999!
1214)171 t mionHHHiinnannaMssssaniiaaMSSi
00 000000 0000 0000 00000000000000000000 00 ollooo
1111 11111111 11111 111 11111111 1 111111 111 111 11 1
222 2 2 2222222222222222 22222222222222222222222
333333333333 3 3 333333333333333333333333333333
44444444444444444444444444444444444444444 4|4
5555555555555555555555555555 5555555555555551
66666666666666666666666666666666666666666666
77777777777777777777777777777777777777177177
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 8
Figure 43
The punch is equipped with a special circuit such that if there is no card in punching position,
a stop control prevents punching, stops the calculator and lights a red signal light. Other than this
circuit to avoid the loss of computed results, the punch wiring is of the standard type described in
the publications of the International Business Machines Corporation.
The moveable column selection contact of the punch is replaced in the print circuit by the print
step counter (PS), (Fig. 38). The print circuit is similar to the punch circuit, but considerably more
complicated due to the fact that the complements on nine as delivered to the print counters must be
inverted and printed in true form. The print circuit is further complicated because of the flexibility
required in the printing operation. For example, the typewriter plugboards provide controls by means
of which zeros may be dropped off to the right and left, decimal points and minus signs may be printed
and the digits of the quantity horizontally spaced as desired. The plugging of the two line step counters
(LS and LS ) controls the vertical spacing of the quantities being printed. All of the plugging neces-
sary to the printing operation is described in detail in Chapter V.
The two print counters (Fig. 38) have complete carry circuits, including end around carry, and
may perform all of the operations of normal storage counters. They consist of twenty-four four
molding counters. The first molding is used for ordinary operations and resets. However, all four
moldings are used to deliver the quantities in the print counter to the magnets which operate the num-
ber keys of the typewriters. Except for these magnets the typewriters (Plate XIV) are standard
96
ELECTRICAL CIRCUITS
writin " machines manufactured fo v the International Business Machines Corporation and described in
detail in that company's publications.
Located just below the typewriters (Plate XIV) are two card feeds. These read quantities from
standard tabulating machine cards (Fig. 43) into the calculator under control of the sequence mecha-
nism . Sequence relays control the pick up of the solenoids directing the downward motion of the card
through the feed and the pick up of the brush control relay. The nine number impulses, provided by
the control cams CC-17, 19, 21 and 23 are routed through a brush to the common roller, (Fig. 44).
CONTROL CAMS
+ FC-17
GUIDE ROLLERS
READING
BRUSH
READ- OUT OF
CARD COLUMN N
BRUSH
RELAY
PLUG
WIRE
BUSS
PATH OF CARD
Figure 44
The reading brush of each card column makes contact with the common roller through the perforations
in the card. The motion of the card between the brushes and the common roller is so timed that the
number impulses and the number perforations in the card are synchronized. From the reading brush,
the impulse travels via the plugging and the brush control relay to the buss. The card feeds are
equipped with an automatic control such that a card jam or lack of cards in the feeds will stop the
97
ELECTRICAL CIRCUITS
calculator and light a red signal light. Like the catrd punch and the typewriters, descriptions of the
card feeds may be found in the publications of the International Business Machines Corporation.
The card feeds are the last of the component parts of the calculator to be described in this
chapter. The discussion of electrical circuits here given is far from complete. It is hoped, however,
that it will furnish an adequate preparation for the coding and plugging procedures to be discussed in
the two following chapters. These, followed by a study of the examples given in Chapter VI, will
enable a mathematician to make full use of the calculator, and to exploit its facilities to the greatest
possible advantage .
98
CHAPTER IV
CODING
"These Babes of Grace should be taught by a master well verst in the cant language
or slang patter, in which they should by all means excel."
Early Elizabethan. Quoted in "Secret and Urgent" by Fletcher Pratt
The basic codes initiating the various available operations of the calculator may be employed
one after another as required in the solution of a problem without further change. However, in order
to attain the maximum speed of computation, full advantage must be taken of the methods of interpo-
sition. These are governed by a set of rules which can best be made clear by the study of a large num-
ber of examples. There are many coding routines, such as that for determining the square root by an
iterative process, which occur so frequently as to make standard coding procedures of real value. This
chapter includes the following sections containing the basic codes and certain of the longer procedures.
Section
Operational Codes
Timing
Switches
Storage Counters
Multiplication
Division
Choice Counter
Automatic Check Counter
Multiple In-Out Counter
Logarithm In-Out Counter
Sine In-Out Counter
High Accuracy Computation
Normalizing Register
Logarithm Unit
Page
Section
99
105
107
109
111
120
129
131
133
137
139
142
159
162
Exponential Unit
Iterative Processes
Sine Unit
Interpolators
Design of Functional Tapes
Methods of Differencing
Central-Difference Interpolation
Newton-Gregory Difference Formula
Subtabulation
Inverse Interpolation
Card Feeds
Card Punch
Printing
Interposition of Machine Stops
Page
165
170
182
185
195
202
206
217
224
227
229
231
236
241
99
SUMMARY OF OPERATIONAL CODES
The operational codes include all codes except those of the switches and the storage counters.
An operational code is defined as automatic if it initiates a process which controls the operation of
the machine for one or more succeeding cycles. A code which is non-automatic is read, acted upon
and the sequence mechanism steps to the next line of coding but does not read it. A non-automatic
code must lie under the control of an automatic code or a Miscellaneous 7 must be added.
Automatic Codes
Stop code. If the control switch on the sequence mechanism is down
and the stop key depressed, the machine will stop on the line follow-
ing the next 87 code.
Read the next line of coding and step to the one beyond. If the control
switch on the sequence mechanism is in the up position and the stop
key down, the machine will stop on the line following the next 7 code.
Punch and complete punching before starting next operation. Stop the
machine if there is no card in punching position.
Print and complete printing before starting next operation. Used
when 752 or 7521 is in the In column.
OUT
IN
MISC.
87
Drop out tape selection relays.
Automatic check.
Interpolator position tape to the closest lower value of the argument.
May replace 61.
Read into EIO counter.
Read into print counter I.
Read into print counter n.
Read into punch counter. Stop the machine if there is no card in
punching position.
7
51
6
61
64
641
741
7432
74321
753
100
CODING
Divide.
TXT
MISC.
76
Multiply.
761
Zl
Logarithm.
762
Exponential.
7621
Interpolate.
763
Sine.
7631
]
Select interpolator I.
7654
Select interpolator Tt.
1
76541
Select interpolator m.
76542
Print counter I half pick-up.
76543
765431
I L.
Read into SIO counter (read-in II, plugged).
Read out of EIO counter.
Read "h" correction into intermediate counter.
8741
832
841
SUMMARY OF OPERATIONAL CODES
Non-Automatic Codes
101
Read out negative absolute value from storage counter.
OUT
IN
MISC.
_..
1
Read out positive absolute value from storage counter.
Invert read-out of IVS or switch.
Reset IC counter.
Reset EIO counter.
Invert read-out of any storage counter or swtteh tsetpt IVS*
Reset SIO counter.
Invert or do not invert read-out of any storage counter or switch
(except IVS) under control of counter 70.
Punch,
Step interpolator I ahead.
Step interpolator II ahead.
Step interpolator m ahead.
Step Interpolator I back
2
21
3
31
33
3*1
432
5
53
531
532
54
102
CODING
Step interpolator n back.
riTTT
in
MISC. '
541 1
Step interpolator m back.
Pick up interpolation sequence control relay.
Reset LIO counter.
542
62
63
1
Read from card feed l 9 *
i r
t 1
1632
Read from card feed II.
6321
Place limitation in division.
643
Place limitation in division.
1
i
6431
Place limitation in division.
6432
Place limitation in division.
1
1
64321
Print on typewriter I.
752
Print on typewriter n.
Read into LIO counter.
Read into normalizing register.
7521
765421
8321
SUMMARY OF OPERATIONAL CODES
103
Special read-in for counter 64 "ganging" carry controls of counters
64 and 65.
OUT
IN
MISC.
87
Special read-in for counter 65 "ganging" carry controls of counters
64 and 65.
Special read-in for counter 68 "ganging" carry controls of counters
68 and 69.
Special read-in for counter 69 "ganging" carry controls of counters
68 and 69.
Read into SIO counter (read-in I, direct).
Read out of LIO counter (plugged read-out).
Read out power of ten from normalizing register.
Read out of SIO counter (read- out n, plugged).
Reset print counter I.
Reset print counter II.
Reset punch counter.
Read out of I VS.
Read tape I.
Read tape n.
871
873
8731
874
831
8321
84
842
8421
843
8431
85
851
1
104
CODING
Read tape HI.
OUT
IN
MISC.
852
Read out of (into) columns 13-24 of counter 71 into (from) columns
13-24 of the buss.
Read out of (into) columns 13-24 of counter 71 into (from) columns
1-12 of the buss.
Low order PQ counter read-out. Read out columns 1-23 and the
algebraic sign of PQ counter . Must directly follow a high order
product-out or a quotient-out.
853
(853)
8531
(8531)
86
l
rtcctu uui ux piini uuuiilcx" 1.
882
Read out of print counter n.
8621
Read out of punch counter.
863
Argument control, drops off zeros to the right.
87
i 1
Turn on typewriter n.
871
Turn on typewriter I.
t r
872
Turn off tvnAwriter TT .
8731
J L
Turn off typewriter I.
Read out of SIO counter (read- out I, plugged).
Read out of SIO counter (read-out in, direct).
8732
874
8741
105
TIMING
(1) The unit of time employed by the machine is the cycle; 200 cycles equal one minute.
(2) Except for certain functional operations, one line of coding corresponds to one cycle of machine
time.
(3) Multiplication requires 8 + n cycles, where n is the number of non-zero digits in the odd or even
columns of the multiplier whichever is the greater. Multiplication consumes a minimum of time
when the multiplier is zero: 8 cycles =2.4 seconds. When the multiplier contains 23 non-zero
digits, maximum time is consumed: 20 cycles = 6.0 seconds.
(4) Division requires 6 + 2n cycles, where n is the number of comparisons for which division is
plugged. Division covers a minimum of time when the operation contains but one subtract cycle:
7 + n cycles: a maximum of time when it is plugged for 23 comparisons and there are no "no
go's": 52 cycles = 15.6 seconds.
(5) Logarithms require 114 + 8n cycles, where n is the number of comparisons for which division
is plugged. The divisions, which are a part of the logarithm sequence, are carried through 23
comparisons unless division is plugged for fewer comparisons. If division is plugged for 23
comparisons, the computation of a logarithm requires at most 298 cycles = 1.49 minutes = 89.4
seconds.
(6) Exponentials require 172 + 2n cycles, where n is the number of comparisons for which division
is plugged. The division, which is part of the negative exponential sequence, is carried through
23 comparisons unless division is plugged for fewer comparisons. If division is plugged for 23
comparisons, the computation requires at most 218 cycles = 1.09 minutes = 65.4 seconds. If
x is known to be positive, the exponential computation is reduced to 167 cycles = 0.835 minutes
= 50.1 seconds.
(7) Sines require 199 cycles = 1,0 minutes = 60 seconds.
(8) Interpolation of order k
(a) Positioning time for any tape is
P = 8 + N(k + 2)/2 cycles, maximum
where N = the number of arguments in the tape
k + 1 = the number of interpolational coefficients including C Q .
(b) Computation time is
C = 7 + k(4 + n') cycles
where k + 1 = the number of interpolational coefficients including C .
If the maximum number of digits in any interpolational coefficient is 2d; i.e., even, then
n' = d.
If the maximum number of digits in any interpolational coefficient is 2d + 1; i.e., odd, then
n' =d+l.
106
CODING
(9) Punching a card through 24 columns and resetting the punch counter requires 10 cycles.
(10) Printing and resetting the print counter requires (10c /27) + 4 cycles, where c is the number of
column selection plughubs up to and including the reset. An allowance of 23 cycles between
prints is sufficient for any printing.
107
SWITCHES
No.
Code
No.
Code
No.
Code
1
741
21
75431
41
7651
2
742
22
75432
42
7652
3
7421
23
754321
43
76521
4
743
24
76
44
7653
5
7431
25
761
45
76531
6
7432
26
762
46
76532
7
74321
27
7621
47
765321
8
75
28
763
48
7654
9
751
29
7631
49
76541
10
752
30
7632
50
76542
11
7521
31
76321
51
765421
12
753
32
764
52
76543
13
7531
33
7641
53
765431
14
7532
34
7642
54
765432
15
75321
35
76421
55
7654321
16
754
36
7643
56
8
17
7541
37
76431
57
81
18
7542
38
76432
58
82
19
75421
39
764321
59
821
20
7543
40
765
60
83
Independent Variable Switch, IVS, Code 8431
(1) In order to check the quantities inserted in switches, these should be printed out before a compu-
tation is begun.
(2) Negative numbers are inserted in switches as complements on nine, or inserted positively and
read out using the invert code.
(3) The number in any switch may be read into any storage counter or, under the operational codes,
into a functional counter.
(4) To invert the read-out of any switch (except IVS), it is preferable to use the operational code 32
instead of the code 21 in the Miscellaneous column. To invert the read-out of the IVS, it is
necessary to use the operational code 21 in the Miscellaneous column.
(5) Since the read-out codes of switches are non-automatic, they require a 7 in the Miscellaneous
column unless they are under the control of a preceding automatic code.
1. Read out sw. A into ctr. B; i.e., add sw. A into ctr. B.
2. Add minus sw. A (except IVS) into ctr. B.
or
3. Add IVS to ctr. B.
OUT
IN
MISC.
A
B
7
A
B
732
A
B
721
8431
B
7
108
CODING
OUT
IN
MISC,
8431
B
721
A
B
7432
4. Add minus IVS to ctr. B.
5. Invert the read-out of sw. A (except IVS) under control
of ctr. 70, and read into ctr. B. See Choice Counter.
(6) If the number of constants desired for a problem exceeds the number of switches, the constants
may be read into storage counters not used in the problem by means of the IVS.
(7) If the number of constants in a problem exceeds the number of switches, they may be placed in
a value tape (see Interpolation) or if all three interpolators are in use, they may be placed in
card feeds or in counters as suggested in note (6),
(8) If a column of a switch is set on either of the blank positions between "0" and "9", numbers will
net be read out of that switch column either normally or with an invert code. For example of
use, see Logarithm In=Out Counter, example 8,
109
STORAGE COUNTERS
No.
Code
No.
Code
No.
Code
1
1
25
541
49
651
2
2
26
542
50
652
3
21
27
5421
51
6521
4
3
28
543
52
653
5
31
29
5431
53
6531
6
32
30
5432
54
6532
7
321
31
54321
55
65321
8
4
32
6
56
654
9
41
33
61
57
6541
10
42
34
62
58
6542
11
421
35
621
59
65421
12
43
36
63
60
6543
13
431
37
631
61
65431
14
432
38
632
62
65432
15
4321
39
6321
63
654321
16
5
40
64
64
' 7
17
51
41
641
65
71
18
52
42
642
66
72
19
521
43
6421
67
721
20
53
44
643
68
73
21
531
45
6431
69
731
22
532
46
6432
70
732
23
5321
47
64321
71
7321
24
54
48
65
72
74
(1) The number in any storage counter may be read into any other storage counter or, under the
operational codes, into a functional counter.
(2) It is good practice to reset a storage counter just before using it. This frequently avoids the
necessity of starting tapes and preserves quantities in the machine as long as possible.
(3) Counters 64, 65, 68, 69, 70, 71 and 72 are wired for special operations. These extra uses do
not invalidate their use as normal storage counters. The details of these extra functions will be
dealt with in sections concerning these counters.
(4) The LIO and SIO counters may be used as normal storage counters and as special counters for
the addition of positive quantities and the shifting of quantities to the right or left. In any case,
they require special codes and plugging. See Logarithm In-Out Counter and Sine In-Out Counter.
(5) Since the read-out and read-in codes of the storage counters are non-automatic, they require a
7 in the Miscellaneous column unless they are under the control of a previous automatic oper-
ational code.
(6) Since the print and punch counters have complete sets of carry controls, including end around
carries, quantities may be read into them as into any storage counter except that their read-in
codes are automatic and must not be followed by a 7 in the Miscellaneous column. The read-in
to the punch counter must not be interposed in multiplication or division. See Printing and Card
Punch.
1. Add ctr. A to ctr. B.
OUT
IN
MISC.
A
B
7
110
CODING
2. Add minus ctr. A to ctr. B.
IN
•utter*
A
B
732
3. Invert the read-out of ctr. A under control of ctr. 70
and read into ctr. B. See Choice Counter.
A
B
7432
4. Add absolute value of ctr. A to ctr. B.
A
B
72
5. Add minus absolute value of ctr. A to ctr. B.
A
i i
B
71
6. Reset ctr. A.
A A 7
Ill
MULTIPLICATION
(1) Multiplication requires plugging to care for the decimal point. See Plugging Instructions.
(2) Numbers may not be read into the multiplying unit from card feeds.
(3) The multiplicand, MC, and the multiplier, MP, may be interchanged without affecting the value
of the product. The number having the fewer non-zero digits should be used as the multiplier.
(4) The read-out of a product may not be inverted. In order to read out a negative product, invert
either the multiplicand or the multiplier.
(5) The product may be read out to a print counter or to the punch counter.
(6) Two lines of coding, not involving the intermediate counter, may be interposed between the read-
in of MC and the read-in of MP. When operations are thus interposed, a 7 is required in the
Miscellaneous column of the line containing the read-in of MC.
If only one line is interposed between MC and MP, it must not contain an automatic code (or a
7 in the Miscellaneous column).
If two lines are interposed between MC and MP, the first must and the second may contain an
automatic code (or a 7 in the Miscellaneous column).
(7) 3 + n lines of coding, not involving the intermediate counter, may be interposed between the
read-in of MP and the read-out of the product. Here n is equal to the number of non-zero
digits in the odd or even columns of MP, whichever is the greater. Where operations are thus
interposed, a 7 is required in the Miscellaneous column of the line containing the read-in of
MP.
If only one line is interposed between MP and the read-out of the product, it must not contain
an automatic code (or a 7 in the Miscellaneous column).
If two or more lines are interposed between MP and the read-out of the product, all but the last
line must contain automatic codes (or 7's in the Miscellaneous column). The line preceding the
read-out of the product must not contain an automatic code.
(8) If a zero MP is possible, no more than three cycles may be interposed between the read-in of
MP and the read-out of the product.
(9) Card feeding, reading into the punch counter or the check procedure may be interposed in multi-
plication only when the coding is specially arranged. See Interposition of Machine Stops.
(10) "Print and complete printing" or "punch and complete punching" should in general not be inter-
posed in multiplication.
1. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C.
OUT
IN
MISC.
A
761
B
C
7
112
CODING
2. Multiply minus sw. (except IVS) or ctr. A by sw. or ctr. B
and deliver the product to ctr. C.
3. Multiply sw. or ctr. A by minus sw. (except IVS) or ctr. B
and deliver the product to ctr. C.
4. Multiply the absolute value of ctr. A by sw. or ctr. B and
deliver the product to ctr. C.
5. Multiply sw. or ctr. A by minus IVS and deliver the
product to ctr. C.
6. Multiply sw. or ctr. A by sw. or ctr. B, read the product
to print ctr. I and print on typewriter I.
7. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose one addition between MC
and MP.
OUT
IN
MISC.
A
761
32
B
C
7
A
761
B
32
C
7
A
761
2
B
C
7
A
761
8431
21
t
C
7
■ i
A
761
B
7432
752
7
A
761
7
D
E
B
C
7
MULTIPLICATION
113
9.
10.
11.
12.
Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose one subtraction between
MC and MP.
Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose two additions between MC
and MP.
Multiply minus sw. (except IVS) or ctr. A by sw. or ctr.
B and deliver the product to ctr. C. Interpose an addition
and a subtraction between MC and MP. Turn on type-
writer I.
Multiply the absolute value of ctr. A by sw. or ctr. B and
deliver the product to ctr. C. Read from ctr. D to print
ctr. I and print on typewriter I with argument control
between MC and MP.
Multiply the negative absolute value of ctr. A by minus
sw. (except IVS) or ctr. B and deliver the product to ctr.
C. Step and read from value tape on interpolator I to ctr.
D, between MC and MP. Turn on typewriter I and turn
off typewriter n.
OUT
IN
MISC.
A
761
7
D
E
32
B
C
7
A
761
7
D
E
7
F
G
B
C
7
A
761
732
D
E
7
F
G
32
B
872
C
7
A
761
72
D
7432
87
752
B
C
7
A
761
71
85
753
872
D
Continued on next page
114
CODING
12. (continued)
13.
Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Step the value tape on interpolator I
twice between MC and MP. Step and read from the tape
to ctr. D and then step twice more between MP and the
read-out of the product. Turn off typewriter I.
14.
Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose one addition between MP
and read-out of product.
15.
Multiply sw. or ctr. A by sw. or ctr. a, reset ctr. C and
deliver the product to ctr. C.
16. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose two additions and two sub-
tractions between MP and read-out of product.
OUT
IN
MISC.
B
32
8731
C
7
A
761
7
753
53
B
7
85
753
D
7
8732
753
53
C
7
l
A
761
1
B
7
D
E
C
7
A
761
B
7
C
C
C
7
A
761
B
7
D
E
7
— ___
Continued on next page
MULTIPLICATION
115
16. (continued)
OUT
IN
MISC.
F
E
7
G
H
732
G
J
32
C
7
17. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose a step and read from a
value tape on interpolator I between MC and MP. Inter-
pose a step and read from a value tape on interpolator I
and an addition and a reset between MP and read-out of
product.
A
761
7
85
753
D
B
7
85
753
E
7
F
G
7
C
C
C
7
18. Multiply plus or minus the quantity in sw. (except IVS)
or ctr. A under control of ctr. 70 by sw. or ctr. B and
deliver the product to ctr. C. Interpose two additions
between MC and MP. Interpose a print, reset of ctr. 70
and addition of an absolute value to ctr. 70 between MP
and read-out of product.
A
761
7432
D
E
7
D
F
B
7
G
7432
752
7
732
732
7
H
732
2
C
7
116
CODING
19.
Multiply sw. or ctr. A by the absolute value of ctr. B and
deliver the product to ctr. C. Interpose read-in and read-
out of LIO between MC and MP. Interpose reset of LIO,
a print and addition of negative absolute value between MP
and read- out of product.
20. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Interpose a print between MC and MP.
Interpose reset of ctr. C and read-in, read-out and reset
of SIO between MP and read-out of product.
OUT 1
TN !
S
MISC.
A
I
761
7
D
765421
7
831
E
B
72
763
E
7432
752
7
F
G
1
C
7
A
761
7
D
7432
752
B
!
7
C
c
7
E
8741
7
8741
F
7
321
c
7
-. .. .,,,■,. ,.._ __i -r ±1 11 ^# nn Jin» raorlinor +Vio X/TT> maw h*» llSpd to Tf»ad the
(11) II necessary, ine Diana, in uuiuuni ut me uuc u» ovmuij ..v^—^t, — —- — j
MP simultaneously to a storage counter, to a print counter or to initiate printing.
21. Multiply sw. or ctr. A by sw. or ctr. B, simultaneously
reading B to C and read the product to D. Note that this
may not be used to reset ctr. B. Print G between read-
ing of A and B. Interpose 4 cycles between read-in of
MP and read-out of product.
OUT
IN
MISC.
A
761
1
G
7432
752
Continued on next page
MULTIPLICATION
117
21. (continued)
22. Multiply sw. or ctr. A by B + C, print G and deliver the
product to ctr. D. Interpose other operations.
23. Multiply sw. or ctr. A by sw. or ctr. B, print B and deliver
the product to ctr. C. Reset ctr. C during multiplication.
Interpose other operations.
OUT
IN
MISC.
B
C
7
85
753
E
7
85
753
F
D
7
A
761
7
C
B
7
G
7432
B
752
7
85
753
E
7
85
753
F
D
7
A
761
7
D
D
7
E
E
B
7432
752
7
C
C
7
F
D
32
C
7
118
CODING
24. Multiply sw. or ctr. A by B which is read from a value
tape. Simultaneously read B to ctr. B and deliver the
product to ctr. C. Reset ctr. C during multiplication.
Note line containing reset of D must be included if only
as line (blank, blank, 7).
25. Multiply sw. or ctr. A by B which is read from a value
TTW-BTfaTeC?
aHH-i-nar ssrsH rocaf r*v«*l^s
OUT
IN
A
761
7
D
D
7
85
B
7
C
C
C
7
A
761
7
rj
rj
7
85
871
7
G
G
7
E
D
7
E
G
872
C
7
(12) If necessary, the blank Out column of the line of coding reading out the product may be used to
select a value tape from which the value is read on the next line, or for turning typewriters on
and off.
26. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Read the value from a tape on interpo-
lator I to ctr. D.
27. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to ctr. C. Read D from a tape on interpolator I
and multiply it by sw, or ctr. E and deliver this product
to ctr. F. Turn off both typewriters.
1
OUT
IN
i
MISC.
A
761
B
85
C
7
D
7
A
761
B
• i
i
Continued on next page
119
MULTIPLICATION
27. (continued)
OUT
IN
MISC.
85
C
7
8731
761
E
8732
F
7
(13) If necessary, the codes for punching and for stepping an interpolator may be placed in the
Miscellaneous column of the lines of coding reading the MP and MC if these lines do not al-
ready contain an invert or other operational code. These codes may also be added in the line
of coding reading out the product.
28. Multiply sw. or ctr. A by the absolute value of ctr. B.
Add A to C and print C with half pick-up on typewriter I.
Step the tape on interpolator I four times and read the
value to D. Step the tape twice more. Reset ctr. C.
Deliver the product to ctr. P and punch out the quantity
in the punch ctr. Turn on typewriter n.
OUT
IN
MISC.
A
761
753
A
C
753
C
7432
53
B
76543
72
85
752
753
D
753
C
C
53
871
P
75
120
DIVISION
(1) Division does not require nluoroin 0, to care for the decimal ™oint
(2) The "Divide N minus Decimal" switch must be set to the value,
N = 22 - K
where K is the number of columns to the right of the decimal point. If the decimal point lies
between columns 23 and 24, division may be performed by setting the "Divide N minus Decimal"
switch to zero and shifting the quotient one column to the left via LIO counter or SIO counter.
There will, however, be no more than 22 decimal places in the result.
(3) The first number read to the dividing unit in the first line of division coding is the divisor, DR.
(4) Numbers may not be read into the dividing unit from the card feeds.
(5) The read-out of a quotient may not be inverted. In order to read out a negative quotient, invert
either the divisor, DR, or the dividend, DD.
(6) The quotient may be read out to a print counter or to the punch counter .
(7) The degree of accuracy in division may be controlled by operational codes and plugging. See
Plugging Instructions. The accuracies available vary with the plugging from one to twenty-three
columns. For a given problem five different accuracies may be selected in this range. If only
one accuracy is needed in a given problem, no code need be used; i.e„ the Miscellaneous column
is "blank". The operational codes of the accuracies are placed in the Miscellaneous column
with either DRorDD read-in or on the lines interposed between them. The codes are 643,6431,
6432, 64321 and "blank". These codes may not be used in combination with an invert or other
operational code. The degree of accuracy of division within the logarithm and exDonential units
is controlled by the plugging of the "blank" code. Not more than 23 digits of any quotient, in-
cluding the first "no go" if any, can be read out of the PQ counter.
(8) Two lines of coding, not involving the intermediate counter, may be interposed between the
read-in of DR and the read-in of DD. When operations are thus interposed, a 7 is required in
the Miscellaneous column of the line containing the read-in of DR.
If only one line is interposed between DR and DD, it must not contain an automatic code (or a 7
in the Miscellaneous column).
If two lines of coding are interposed between DR and DD,the first must and the second may con-
tain an automatic code (or a 7 in the Miscellaneous column).
iQl T+ io nnociKlo t/-v I'ntaimncia v> ■ 1 li~>nc nt ^ n JJ_~ _„J- i_ 1 J 1.1 u;_i_ j. . _» _ .x . .
X w, ». ,~ i,«,w^»»,*^ w uttv.puoc ix -r j. nuco ui v-isuiug, iifjx. mvui.viug me uiiuupiy-aiviae unit, Deiween
the read-in of DD and the read-out of the quotient. Here n is equal to the number of compari-
sons for which division is plugged. Where operations are thus interposed, a 7 is required in
the Miscellaneous column of the line containing the read-in of DD.
If only one line is interposed between DD and the read-out of the quotient, it must not contain an
automatic code (or a 7 in the Miscellaneous column).
If two or more lines are interposed between DD and the read-out of the quotient, all but the last
line must contain automatic codes (or 7's in the Miscellaneous column). The line preceding the
read-out of the quotient must not contain an automatic code.
(10) Card feeding, reading to the punch counter or the check procedure maybe interposed in division
only when the coding is specially arranged. See Interposition of Machine Stops.
121
DIVISION
(11) "Print and complete printing" or "punch and complete punching" should in general not be
terposed in division.
1. Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C.
2. Divide minus sw. (except IVS) or ctr. A by sw. or ctr.
B and deliver the quotient to ctr. C.
3. Divide sw. or ctr. A by minus sw. (except IVS) or ctr.
B and deliver the quotient to ctr. C.
4. Divide the absolute value of ctr. A by sw. or ctr. B and
deliver the quotient to ctr. C.
5. Divide sw. or ctr. A by minus IVS and deliver the
quotient to ctr. C.
OUT
IN
MISC.
B
76
A
C
7
B
76
A
32
C
7
B
76
32
A
C
7
B
76
A
2
C
7
8431
76
21
A
C
7
6. Divide sw. or ctr. A by sw. or ctr. B with accuracy
6431 and deliver the quotient to ctr. C.
or
B
76
6431
A
C
7
B
76
A
6431
C
- .
7
122
CODING
7.
Divide minus sw. (except IVS) or ctr. A by sw. or ctr. B
with accuracy 6432 and deliver the quotient to ctr. C.
8.
Divide sw. or ctr. A by minus sw. (except IVS) or ctr. B
with accuracy 64321 and deliver the quotient to ctr. C.
Divide sw= or ctr. A by sw* or ctr s B and read the quotient
to print ctr. I and print on typewriter I.
10. Divide sw. or ctr. A by sw. or ctr. B with accuracy 643 and
deliver the quotient to ctr. C. Interpose one addition be-
tween DR and DD. Turn on typewriter I.
11.
Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C. Interpose one subtraction between
DR and DD.
12.
Divide sw. or ctr.
quotient to ctr. C.
and DD.
A by sw. or ctr. B and deliver the
Interpose two additions between DR
r\TTT>
IN
MISC.
B
76
6432
A
32
C
7
B
76
32
A
64321
C
7
B
76
A
7432
752
7
1
B
76
7643
D
E
A
872
c
7
I
B
76
7
D
E
32
A
c
7
B
76
7
D
E
7
F
i i
G
-i
Continued on next page
DIVISION
123
12. (continued)
15.
16.
13. Divide minus sw. (except IVS) or ctr. A by sw. or ctr. B
with accuracy 6431 and deliver the quotient to ctr. C. In-
terpose an addition and a subtraction between DR and DD.
14. Divide the absolute value of ctr. A by sw. or ctr. B and
deliver the quotient to ctr. C. Read from ctr. D to print
ctr. I and print on typewriter I between DR and DD.
Divide the negative absolute value of ctr. A by minus sw.
(except IVS) or ctr. B and deliver the quotient to ctr. C.
Step and read from value tape on interpolator I to ctr. D
between DR and DD.
Divide sw. or ctr. A by sw. or ctr. B with accuracy 6432
and deliver the quotient to ctr. C. Step the value tape on
interpolator I twice between DR and DD, read from the
tape and step twice more between DD and the read-out of
the quotient.
OUT
IN
MISC.
A
C
7
B
76
76431
D
E
7
F
G
32
A
32
C
7
B
76
7
D
7432
752
A
2
C
7
B
76
732
85
753
D
A
1
C
7
B
76
76432
753
53
A
7
85
7
Continued on next page
124
CODING
16. (continued)
17. Divide sw. or ctr. A by sw. or ctr. B with accuracy 64321
and deliver the quotient to ctr. C. Interpose one addition
between DD and the read -out of the quotient.
18. Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C. Reset ctr. C between DD and the read-
out of the quotient.
19. Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C. Interpose eight adding and resetting
operations between DD and the read-out of the quotient.
OUT
IN
MISC.
D
7
753
53
C
7
B
76
64321
A
7
D
E
C
7
B
76
A
7
C
C
C
7
B
76
A
7
D
E
7
n
F
7 i
D
G
7
H
H
7
I
J
I
7
J
7
D
H
72
A
H
2
C
7
DIVISION
125
20. Divide plus or minus the quantity in ctr. A under control
of ctr. 70 by sw. or ctr. B, with accuracy 643, and deliver
the quotient to ctr. C. Interpose two additions between DR
and DD. Interpose a print of ctr. A under control of ctr.
70, reset of ctr. 70, addition of an absolute value to ctr.
70 and addition of ctr. G to ctr. 70 between DD and read-
out of quotient.
OUT
IN
MISC.
B
76
7643
D
E
7
D
E
A
7432
A
7432
432
752
7
732
7*32
7
F
732
72
G
732
C
7
21. Divide sw. or ctr. A by the absolute value of ctr. B with
accuracy 6431 and deliver the quotient to ctr. C. Inter-
pose a print of ctr. A between DR and DD. Interpose a
read-in, read-out and reset of LIO and additions into LIO
between DD and read-out of quotient.
B
76
72
A
7432
752
A
76431
D
765421
7
831
E
7
763
F
765421
7
G
765421
C
7
(12) If necessary, the blank In column of the line of coding reading the DD may be used to read the
DD simultaneously to a storage counter, to a print counter or to initiate printing.
22. Divide sw. or ctr. A by sw. or ctr. B, with accuracy 6432,
simultaneously reading A to C and deliver the quotient to
ctr. D. Note that this may not be used to reset A.
OUT
IN
MISC.
B
76
6432
A
C
Continued on next page
126
CODING
22. (continued)
or
23. Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C. Print A with half pick-up between
DR and DD. This operation may also be coded by omit-
ting the first 7 and the second A.
24.
25.
Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr, C. Print A. Reset ctr. C during di-
vision. The number of cycles interposed between the
read-in of DD and the read-out of the quotient is de-
pendent upon the division accuracy plugging.
Divide A, which is read from a value tape, by sw. or
ctr. B and deliver the quotient to ctr. C. Simultaneously
read A to ctr. A. Reset ctr. C between DR and DD. The
number of cycles interposed between the read-in of DD
and the read-out of the quotient is dependent upon the
division accuracy plugging.
OUT
IN
MISC.
D
7
B
76
A
C
6432
D
7
B
76
7
A
7432
76543
A
752
C
7
B
76
A
7432
752
7
D
C
E
7
C
7
F
E
732
G
E
7
A
G
C
i
7
B
76
7
C
C
7
85
A
7
D
D
7
Continued on next page
DIVISION
127
25. (continued)
OUT
IN
MISC.
E
D
C
7
26.
Divide A, which is read from a value tape, by sw. or ctr.
B and deliver the quotient to ctr. C. The number of cycles
interposed between the read-in of DD and the read-out of
the quotient is dependent upon the division accuracy plug-
ging.
B
76
7
D
D
7
85
7
G
G
7
E
D
7
E
G
C
7
27.
Divide A, which is read from a value tape, by minus ctr.
B with accuracy 6432 and deliver the quotient to ctr. C.
The number of cycles interposed between the read-in of
DD and the read-out of the quotient is dependent upon the
division accuracy plugging.
B
76
732
D
D
7
85
76432
G
G
7
E
D
7
E
G
7
F
G
C
7
(13> IS? V* "f* 0ut ,. c ° lumn ° f °>e «ne of coding reading out the quotient may be used to
selecta value tape from which the value is read on the next Une or forlrning liters on
28. Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C. Read value from tape on interpo-
lator I to ctr. D.
OUT
IN
MISC.
B
76
A
Continued on next page
128
CODING
28. (continued)
29. Divide sw. or ctr. A by sw. or ctr. B and deliver the
quotient to ctr. C. Read D from a tape on interpolator I
and multiply it by sw. or ctr. E, deliver this product to
ctr. F. Turn off typewriter I.
OUT
IN
85
C
7
D
7
B
76
A
85
C
7
761
E
8732
T?
7
(14) If necessary, the codes for punching and for stepping an interpolator may be placed in the
Miscellaneous column of the lines of coding reading the DR and DD if these lines do not al-
ready contain an invert or other operational code. These codes may also be added in the line
of coding reading out the quotient,
30. Divide minus sw. (except IVS) or ctr. B by sw. or ctr. A
with accuracy 643, deliver the quotient to ctr. C and punch
out the quantity in the punch ctr. Turn on typewriter I.
OUT
IN
MISC.
A
76
643
B
32
872
C
75
129
CHOICE COUNTER
(1)
(2)
(3)
(4)
(5)
Counter 70
The special controls on counter 70 make it possible to reverse the algebraic sign of a quantity
if and only if some second quantity standing in counter 70 is negative (including the quantity
minus zero).
OUT
IN
MISC.
A
B
7432
1. Invert the read-out of sw. (except IVS) or ctr. A to ctr. B
if and only if the quantity standing in ctr. 70 is negative.
Counter 70 may be used to roundoff numbers to n places of accuracy by addition or subtraction
of 5 x 10" ( n + 1/ according as the given number is positive or negative. The resulting number
may then be printed with the (n + l)st, (n + 2)nd, ... places cut off by typewriter plugging. This
may substitute for the half pick-up discussed under Printing.
2. Round off the number in ctr. A to n places, where
5 x 10" ' n + l) is in sw. B and print on typewriter I.
OUT
IN
MISC.
A
732
7
B
732
7432
732
7432
752
7
For punched cards not to be fed to the machine for further computation, counter 70 may be used
to round off to n places of accuracy as in note (2). The extra places are cut off by punch plug-
ging. If the cards are to be fed to the machine for further computation, 5 x 10~( n + 1) must be
added in all cases. See Multiple In -Out Counter, note (6).
Any computation involving an odd function f (x) = - f(-x), may be simplified by use of counter
70. For example, if sin x is to be computed by interpolation, the functional tape need only be
punched for positive arguments, the quantity x read to counter 70 and the result of interpolation
read out of a storage counter under control of counter 70. See Interpolators.
The choice counter may be used to compute various types of discontinuous functions and functions
with discontinuous derivatives . Suppose it is desired to compute
F(x) = f^x),
x sa,
F(x) = f 2 (x),
a<x.
Calculate
Sl =f 2 + f l
&2 = f 2 " f 1
and store x - a in counter 70.
Compute 2F(x) = gj ± g 2 under control of counter 70.
Thus if x < a, x - a < -0,
F(x) = f x (x) = ( gj - g 2 )/2 .
130
CODING
If x>a, x - a>0,
F(x) = f 2 (x) = (g x + g 2 )/2.
Repetition of this process will care for functions with any desired number of discontinuities,
or discontinuities of their derivatives.
Suppose
F(x)=f(x), x <a,
F(x)=yx), a<x<b,
F(x) = f 3 (x), b<x.
Calculate
*1 = f 2 + f x
^2 = f 2 " f l
and store x - a in counter 70.
Compute 2F 1 (x) = g^± g 2 under control of counter 70.
Calculate
rr — f . -C
&3 - * 3 t x x
H-h- F i
and store x - b in counter 70.
Compute 2F(x) = g g ± g 4 under control of counter 70.
While this is the basic coding for such functions, in many cases it is possbile to shorten the
calculation depending upon the form of the functions.
131
AUTOMATIC CHECK COUNTER
Counter 72
(1) The special controls on this counter insure that the absolute value of a given number is less than
another given positive number or tolerance. If this condition is not satisfied, the machine is
stopped.
1. To check the absolute value of the quantity in ctr. A against
the positive tolerance in sw. or ctr. B.
(3)
(4)
(5)
(6)
(7)
To insure that +0 £ A -= B, check the quantity in ctr. A
against the positive tolerance in sw. or ctr. B.
(2) The first line of the check coding may be separated from the other two.
OUT
IN
MISC.
B
74
7
A
74
71
74
74
64
B
74
7
A
74
732
74
74
64
The last two lines of the check coding may not be separated. The machine stops on the line fol-
lowing a 64 code unless in the preceding cycle there is an end around carry in counter 72.
The last line of the check coding includes the reset of the check counter as well as the 64 code
for the check operation. It is possible incase of necessity to omit the reset of the check counter
and use this space for another reset or an addition. In this eventuality the check counter must
be reset before using it again.
It is always desirable to print out the quantity being checked before it is routed through the check
counter. Thus in case of failure to check, the magnitude and type of error readily may be ob-
served.
If possible, all essential parts of a computation should be preserved in the machine until the
check has been made. Thus in case of machine error, the elements can be read out and manual
computation used to aid in detecting the error.
The consumption of machine time must enter into the choice of checking methods. If a final
check can be devised for an entire computation when the time is half an hour or less per run,
intervening check computations may well be omitted. If each element of out-put is independent,
each should be checked. If a run continues more than half an hour, checks should be inserted at
intermediate points.
(8) The most commonly used methods of checking are:
(a) Inverse Operation
If y = f(x) is computed, then a check of x - x', where x 1 = f -1 (y), against a preassigned
tolerance will in general give an adequate check. If y = x*/ n is computed by iteration or
logarithms, n being an integer, then x - x 1 , where x' = y n as computed by multiplication,
is a check making use of distinct machine processes .
(b) Independent Calculation
In some cases it is possible to derive two independent methods of computing f(x) which
may be checked against each other.
132
CODING
(c) Interchange of counters
If no brief method of check can be devised, the computation may be repeated using differ-
ent storage or functional counters . In checking multiplication, the multiplier and multiplicand
may be interchanged. The problem may be rerun with a different decimal point or with
certain values multiplied or divided by powers of ten. This will shift digits into different
columns of the storage and functional counters.
(d) Identities
In many cases functions satisfy certain identities or recursion formulae which maybe used
as checks. For example, the computation of sin x and cos x may be checked by:
. 2 2
sin x + cos x
1 = 0.
It should be noted, however, that this particular identity will not detect compensating errors.
(e) Differences
Standard differencing techniques provide a basic method of checking. If one of the higher
rfl*ffoT»on*»oc rvf o ■FitTi/»f"i nr\ f*r\Y\fni*YY\c +r\ *»
viAa* Xfeti
f»0 1 ITT thO
use of differencing techniques defends u~on the amount of information available concerning
the function and its differences.
(f ) Gross Checks
Observation of the trend of a function and rough differencing, together with graphing, will in
many cases provide gross checks.
(9) The checking of value and functional tapes, cards and printed data is considered in their re-
spective sections. See Design of Functional Tapes, Card Feeds, Card Punch and Printing.
(10) If the choice counter is used in conjunction with the check procedure, it is possible to deter-
mine whether or not two given quantities having the same sign differ by not more than one
in a given significant digit.
If the quantities A, 10000 > A ^ 1, and E, lying in ctrs.
A and B, are of the same sign, the following coding will
insure that A and B differ by less than one in the fifth
significant digit. Ctrs. C, 70 and 72 are reset and
available for computation.
Switch ST = 10
SU = 90
SV = 900
ow — n ni;nnR
sx
=
0.00045
SY
=
U.UU45
sz
=
0.045
I 1
OUT | IN
i 1
MISC.
A
732
71
ST
732
732
SW
C
7
SX
C
7432
OTT
woo
1 OCi
t700
10£
SY
c
7432
SV
732
732
SZ
C
7432
A
B
732
C
74
7
B
74
71
§4
133
MULTIPLE IN-OUT COUNTER
(1) This counter is equipped with multiple in-out relays as follows:
(a) From columns 1-24 of the buss into columns 1-24 of the counter in normal position, code
7321 in the In column.
(b) From columns 1-24 of the counter into columns 1-24 of the buss in normal position, code
7321 in the Out column.
(c) From columns 13-24 of the buss into columns 13-24 of the counter, code 853 in the In
column.
(d) From columns 13-24 of the counter into columns 13-24 of the buss, code 853 in the Out
column.
(e) From columns 1-12 of the buss into columns 13-24 of the counter, code 8531 in the In
column.
(f) From columns 13-24 of the counter into columns 1-12 of the buss, code 8531 in the Out
column.
(2) Columns 13-24 of the MIO counter may be reset using the code 853 in the Out and In columns.
(3) The effect of this counter is to double the number of storage counters in the machine, each
storage counter having a capacity of 12 columns. Essentially, only the upper half is used in
this process, since there is no special read-out of the lower 12 columns. The lower half of
MIO may not be used for adding negative numbers, since there is no carry from column 12
to column 1. All adding which involves any negative numbers must be done in the upper half
of the counter, which is supplied with a special carry from column 24 to column 13.
(4) If both of the numbers stored in a counter by means of the MIO counter are positive, they may
be simultaneously multiplied by a third positive quantity. This process is frequently of use in
dealing with statistical data.
(5) The special controls on counter 71 do not invalidate its use in the normal manner, when the
code 7321 is used.
1. Sw. A and sw. B each contain two numbers, one in cols. 1-12,
and the other in cols. 13-24, cols. 12 and 24 containing the
algebraic sign. It is required to add together the numbers
in corresponding columns of the two switches and deliver
the two sums to ctr. C in corresponding columns. Both
sums are to be printed in cols. 1-12 by typewriter I.
OUT
IN
MISC.
7321
7321
7
A
853
7
B
853
7
853
C
7
8531
7432
752
6
7321
7321
7
A
8531
7
Continued on next page
134
CODING
1. (continued)
OUT
IN
MISC.
B
8531
7
8531
C
7
8531
7432
752
6
(6) The MIO counter may be used to round off numbers to be punched in cards. The number is
shifted by the LIO counter so that the columns to be punched appear in columns 13-24 of the
MIO counter. Two cases then arise depending on whether the cards are to be used in further
calculations or not.
(a) If the cards are not to be used in further calculations in the machine, but simply printed
out or used for checking purposes, a five is added or subtracted from the 12th column ac-
cording as the number is positive or negative under the control of counter 70. Columns
13-24 of the MIO counter are read to the punch counter.
2. The number in ctr. A is to be rounded off and punched in
cols. 1-12 of a card. Sw. B contains a five in col. 12.
OUT
IN
MISC.
A
732
7
A
765421
7
831
7321
7
B
7321
7432
853
753
51
(b) If the cards are to be fed to the machine for use in further calculations, a five is added
in the 12th machine column. Columns 13-24 of the MIO counter are read to the punch
counter
111C ilUlUUCl U* WIJ. i
+A Ko waiwiHoH r\ff 0¥>«4 rmr»/»Vio/1 in
cols. 1-12 of a card for further computation. Sw. B
contains a five in col. 12.
OUT
IN
1
MISC.
_A
765421
7
831
7321
7
B
7321
7
853
753
51
The MIO counter may be used tc produce serial numbers for sorting punched cards. A deck
is to be punched with values of several functions; e.g., f(x), g(x), h(x), in the order f(x_ _<),
g(x_ J, h(x n ), f(x), g(x), h(x), f(x ni1 ), g(x ni1 ), M*^), etc. The cards are later to be
135
MULTIPLE IN-OUT COUNTER
(8)
sorted according to the magnitude of the first four digits of f(x). There are not more than eleven
significant digits in each of the functions to be punched. The functions are sent to columns 13-
24 of the MIO counter. The first four columns of f(x) are selected by routing through the LIO
counter to columns 6-9 of the MIO counter. The serial numbers within the group are delivered
from an accumulation counter to the low order columns of the MIO counter. Columns 1-24 of
the MIO counter are then delivered to the punch counter. Thus if
f(x) = 23.137 564 76
g(x) = 0.249 301 24
h(x) = 1.656 837 96,
the three cards punched will read,
023 137 564 760 002 313 000 01
000 247 301 240 002 313 000 02
001 656 837 960 002 313 000 03.
4. Read g(x) from ctr. A to cols. 13-24 of MIO. Read the
first four digits of f(x) from ctr. B via LIO to cols. 6-9
of MIO. Read the serial number within the group from
ctr. C and punch the cards.
OUT
IN
MISC.,
A
853
7
B
765421
7
831
7321
7
C
7321
7
7321
753
51
The MIO counter may be used to drop off digits to the left; i.e., columns 1-12 of a number may
be retained. See also Logarithm In-Out Counter, note (4), and Sine In-Out Counter, note (4).
(a) If the number is positive, read it into the MIO counter with the columns to be dropped in
columns 13-24. Reset columns 13-24 of MIO.
5. Read the number in ctr. A to MIO. Reset cols. 13-24 of
MIO. Read result to ctr. B.
(b) If the sign of the number A is unknown, read it into the MIO counter with the columns to
be dropped in columns 13-24. Reset columns 13-24 of MIO. Read columns 1-12 of MIO
direct to B. Supply nines when needed with negative numbers by reading columns 13-24
of MIO to B under control of counter 70.
6. Read the number in ctr. A to MIO. Reset cols. 13-24 of
MIO. Read result to ctr. B. Supply nines when needed
with negative numbers by reading cols. 13-24 of MIO to
ctr. B under control of ctr. 70.
OUT
IN
MISC.
A
7321
7
853
853
7
7321
B
7
OUT
IN
MISC.
A
7321
7
853
853
7
Continued on next page
136
CODING
6. (continued)
OUT
IN
MISC.
7321
B
7
A
732
7
853
B
7432
137
LOGARITHM IN-OUT COUNTER
(1) The logarithm in-out counter, LIO counter, may be used as a storage counter if necessary. It
requires certain special codes, and plugging. See Plugging Instructions.
1. Read from ctr. A into LIO.
OUT
IN
MISC.
A
765421
7
2. Read from LIO into ctr. B. Plugged read-out.
831
B
7
3. Reset LIO.
763
(2) The LIO counter may not be used for addition unless all of the numbers involved are positive,
since this counter has no end around carry.
(3) The LIO counter maybe used to shift numbers to the right or left, since it has a pluggable read-
out to the buss. If negative numbers are involved, they may not be shifted more than ten columns
to the right on reading out, since only ten nines are available to be plugged in at the left. See
Plugging Instructions.
(4) The LIO counter may be used to drop off digits to the right or left, since it has a pluggable read-
out. Care must be taken to supply nines in dropping digits from negative numbers. See Plug-
ging Instructions.
(5) If it is desired to superpose numbers, the LIO counter may be used to shift one of them. See
Plugging Instructions. A and B are two arguments with the same decimal point. Superpose B
on A to prepare for printing both arguments in one typing operation. If A = 27 and B = 32, the
combination is printed as 32000027 in one typing operation.
4. Shift the number in ctr. B and superpose it on the number in
ctr. A. Print on typewriter I.
OUT
IN
MISC.
B
765421
7
831
A
7
A
7432
63
752
7
(6) The LIO counter may be used as a "doubling" counter to build up simple multiples of a posi-
tive quantity, especially products by powers of two. These operations may be interposed in
other multiplications or in division.
5. x lies in ctr. A. Read 8x to ctr. B.
OUT
IN
MISC.
A
765421
7
831
765421
7
Continued on next page
138
CODING
5. (continued)
AtTT
TXT
1V11UV *
831
765421
7
831
765421
7
831
B
7
(7) The LIO counter reset does not involve the buss .
(8) If more than ten nines are needed for reading out negative numbers from the LIO counter they
may be supplied from a switch under control of the choice counter. If 13 nines are needed in
columns 11-23, ten of them are supplied by plugging to ten columns, say 14-23, and three are
supplied from a switch to columns 11-13.
T^fij*^ y f-M^wj "i"?* A Its f*i"T* Y\ *^hi'ft'iT»2 p ^ ^ columns ^o
right. Sw. P has 000 in cols. 11-13. The other columns
of sw. P (cols. 1-10 and 14-24) are set on the blank
position (not zero). Nines are plugged to cols. 14-23.
The algebraic sign, col. 24, is bottle -plugged as usual.
OUT
IN
MISC.
A
765421
7
831
B
7
B
732
7
P
B
7432
139
SINE IN-OUT COUNTER
(1) The sine in-out counter, SIO counter, may be used as a storage counter if necessary. It re-
quires certain special codes and plugging. See Plugging Instructions.
(2) The SIO counter should not be used independently of the sine computation unless the "85-1 P.U."
switch is in the off position. This switch is at the left hand end of row 21 of the Multiply-Divide
relay panel. If the switch is thrown off, it should be entered in the log, since it is necessary
that the relay be in operation for a sine computation.
1. Read out of ctr. A into SIO. Direct read-in I, no carry;
may not be used for doubling.
2. Read out of ctr. A into SIO. Plugged read-in n, with
carry in all columns except from col. 23 to col. 24 and
col. 24 to col. 1. Automatic Code.
OUT
IN
MISC.
A
874
7
A
8741
(3) If the "SIO-OUT-2 Invert Control" switch is in the on position, a nine in the 24th column will
pick up nines from the ten left hand plughubs of row 40 of the functional plugboard and will in-
vert the read-out of those columns of SIO which are plugged to the buss. If the "SIO-OUT-2
Invert Control" switch is in the off position, a nine in the 24th column will pick up nines from
the plugboard, but the read-out from the SIO will be direct.
3. Read out of SIO into ctr. B. Plugged read-out n.
(4) The plugged read-out I reads directly from the SIO counter, through the plug wires, into the
buss and will not pick up nines from row 40 of the plugboard.
OUT
IN
MISC.
84
B
7
4. Read out of SIO into ctr. B. Plugged read-out I, no nines.
(5) The direct read-out III is completely independent of all plugging.
5. Read out of SIO into ctr. B. Direct read- out HI.
OUT
IN
MISC.
874
B
7
8741
B
7
(6) The SIO counter reset, a Miscellaneous code, does not involve the buss and may therefore be
added to any line of coding not already containing a Miscellaneous code.
6. Reset SIO.
OUT
IN
MISC.
7321
140
CODING
(7) The SIO counter may not be used for addition unless all of the quantities involved are positive
and plugged read-in II is used, since this counter has no carry into the 24th column and no end
around carry.
(8) The SIO counter may be used to shift positive numbers to the right or left, since it has a plug-
gable read-in from the buss and two pluggable read-outs to the buss.
7. Shift the positive quantity standing in cols. 13, 14, 15
and 16 of ctr. A to cols. 3, 4, 5 and 6 of ctr. B.
or
or
OUT
IN
MISC.
A
874
7
84
B
7
A
874
7
874
B
7
A
8741
8741
B
7
(9) The SIO counter may be used to drop off digits to the right or left of quantities, since it has a
pluggable read-out which supplies nines.
8. The last five digits of the quantity standing in ctr. A
contain the code numbers controlling the punched
cards. It is desired to read the function to ctr. B
and the code to ctr. C.
OUT
IN
MISC.
A
874
7
874
B
7
84
rr
I
(10) The SIO counter may be used as a "doubling" counter to build up simple multiples of a positive
quantity, especially products by powers of two, if plugged read-in II is used. These operations
may be interposed in other multiplications or in divisions.
9. x lies in ctr. A. Read 4x to ctr. B.
OUT
IN
MISC.
A
8741
8741
8741
8741
8741
8741
B
7
141
SINE IN-OUT COUNTER
(11) The SIO may be used with the normalizing register to shift quantities from the standard po-
sition in the machine to read out of columns 20 and up. This must be done to facilitate the
printing of the argument of a function in the required columns to conform with the read-out of
the exponent computed in the normalizing register.
10. Ctr. A contains the argument x with decimal point in
the operating position between cols. 15 and 16. Shift
x so that it will be printed with decimal point between
cols. 19 and 20, and print on typewriter I.
OUT
IN
MISC.
A
874
7
874
7432
752
7
142
HIGH ACCURACY COMPUTATION
» A 9 ***
v^uuniers ot ana oo
(1) It is possible to carry on computations covering 46 columns and the algebraic sign.
(2) Special controls are available on the pairs of counters (65, 64) and (69, 68) which make possible
their use as two single adding counters. Counters 65 and 69 contain the high order columns
24-46; 64 and 68, the low order columns 1-23. All additions and subtractions of 46 column num-
bers must be performed in one of these pair of "ganged" counters.
(3) Such numbers are stored across two switches, for example A and B. The algebraic sign is
stored in the 24th column of both switches. Columns 1-23 of the number are stored in columns
1-23 of switch B and columns 24-46 of the number in columns 1-23 of switch A.
(4) If such numbers are to be fed to the machine from cards or a value tape, two entries are re-
quired similar to those used in storing in switches .
(5) 46 column numbers are stored across two storage counters A and B with the algebraic sign in
the 24th column of both counters, columns 1-23" of the number in columns l-23~ of counter B,
and columns 24-46 of the number in columns 1-23 of counter A.
(6) The numbers are stored across any pair of storage counters by reading in each half separately
to the two counters. These read-ins are subject to any of the usual operational codes.
1. A quantity lies across sws. or ctrs. (A,B); read it across
ctrs. (C,D).
2. Invert the read-out of the quantity across sws. or ctrs.
(A,B) into ctrs. (C,D).
(A,B) into ctrs. (C,D) under control of ctr. 70.
4. Read the absolute value of the quantity across ctrs.
(A,B) into ctrs. (C,D).
5. Read minus the absolute value of the quantity across
ctrs. (A,B) into ctrs. (C,D).
OUT
IN
MISC.
A
C
7
B
D
7
A
C
732
B
D
732
A
B
D
7432
A
C
72
B
D
72
i
A
C
l
71
B
D
71
HIGH ACCURACY COMPUTATION
143
(7)
(8)
6. A quantity lies across ctrs. (A,B); reset the ctrs.
7.
8.
A quantity is stored across two cards, high order columns
in feed I and low order columns in feed II; read the quantity
into ctrs. (C,D).
A quantity is stored across two cards in feed I, high order
column card preceding low order column card; read the
quantity into ctrs. (C,D).
A quantity is stored in two entries in a value tape on in-
terpolator I, high order columns preceding low order
columns; read the quantity into ctrs. (C,D).
OUT
IN
MISC.
A
A
7
B
B
7
C
7632
D
76321
C
7632
D
7632
85
7
85
C
753
D
753
The special carry controls of the "ganged" counters are such that column 23 of the low order
counter will carry to column 1 of the high order counter. Column 23 of the high order counter
will carry to column 24 of both of the counters. Column 24 of the high order counter has an
end around carry to column 1 of the lower order counter. The special codes operating these
carry controls are an 8 combined with the normal read-in codes of the counters in the In
columns .
The special controls on counters 64, 65, 68 and 69 do not invalidate their use as normal storage
counters. For usual operations, read-ins, read-outs and resets, the codes 7, 71, 73 and 731 of
the respective counters apply.
10. Add the quantities stored across sws. or ctrs. (A,B),
(C,D) and (E,F), deliver the sum to ctrs. (G,H). Use
"ganged" ctrs. (69,68) for addition.
OUT
IN
MISC.
A
731
7
B
73
7
C
8731
7
D
873
7
E
8731
7
F
873
7
731
G
7
73
H
7
144
CODING
11. Subtract the quantity across sws. or ctrs. (C,D) from the
quantity across sws. or ctrs. (A,B) and deliver the dif-
ference to ctrs. (E,F). Use "ganged" ctrs. (65,64) for
subtraction.
OUT
IN
MISC .
A
71
7
B
7
7
G
871
732
D
87
732
71
E
7
7
F
7
(9) In order to use counter 70 as a sign control counter either the high order columns or the low
order columns of the 46 column number may be read into counter 70, since both are prefixed
by the algebraic sign.
12. Read the quantity stored across sws. or ctrs. (C,D) to
ctrs. (E,F) under control of the algebraic sign of the
number stored across ctrs. (A,B).
OUT
IN
MISC.
A
732
7
C
E
7432
D
F
7432
(10) In using the "ganged" counters in multiplication, the operating decimal point of the machine
must lie between columns 46 and 47; i.e„ between columns 23 and 24 of the high order counter.
Therefore, computations in most cases must be normalized.
(11) The automatic check counter may be used in high accuracy computation if comparisons are
made with known tolerances .
(a) If the tolerance is greater than or equal to 10~23 it is necessary to check the high order
columns only.
13. Check the quantity across ctrs. (A,B) against a tolerance
^ 10-23 i n sw . p.
1
OUT
IN
1
MISC.
P
74
7
A
74
71
74
74
64
(b) If the tolerance is less than lO""* it is necessary tocheckthat the high order columns are
all zero and that the low order columns are less than the tolerance.
HIGH ACCURACY COMPUTATION
145
14. Check the quantity stored across ctrs. (A.B) against a
tolerance <10~23in sw. Q. Sw. P = 10~23.
OUT
IN
MISC.
P
74
7
A
74
71
74
74
64
Q
74
7
B
74
71
74
74
64
(12) To read a 46 column product out of the PQ counter special plugging is required. See Plugging
Instructions.
(13) In general, all products involving 46 column numbers must be accumulated in one of the pairs
of "ganged" counters using the special carry controls and the special product read-out. The
error of this product is not more than 3 in the lowest order column.
(14) The code 873 or 87 in the In column of the line of coding reading out the product reads columns
24-46 of PQ to columns 1-23 of counter 68 or 64, and the sign column of PQ to column 24 of
counter 68 or 64 respectively.
(15) The code 8731 or 871 in the In column of the line of coding reading out the product, followed
immediately by the line (86, 873, 7) or (86, 87, 7), reads the sign column of PQ to column 24 of
both counters 68 and 69 or 64 and 65, columns 24-46 of PQ to columns 1-23 of counter 69 or 65
and columns 1-23 of PQ to columns 1-23 of counter 68 or 64 respectively.
(16) The special carry controls operate throughout these processes, permitting the accumulation of
the product.
(17) Let (A, B) and (C, D) indicate two 46 column numbers stored across these pairs of counters
(high order columns in A and C).
(a) If all the numbers in a computation are known to be positive, the product (A, B) x (C, D) is
built up as follows:
Columns 1-46 of A x C to columns 1-23 of the high order and 1-23 of the low order "ganged"
counters under the special product read- out.
Columns 24-46 of A x D to columns 1-23 of the low order "ganged" counter under the spe-
cial carry controls.
Columns 24-46 of B x C to columns 1-23 of the low order "ganged" counter under the spe-
cial carry controls.
146
CODING
15. Multiply (A,B) by (C,D) and deliver the product to ctrs.
(69,68). All values positive. Lines where operations may
be interposed are left clear. 7's required if operations
are interposed are given as (7).
OUT
IN
MISC.
A
761
(7)
C
(7)
8731
7
86
873
7
A
761
(7)
D
(7)
!
873
7
B
761
(?)
C
(7)
873
7
(b) If some of the numbers in a computation may be negative, the product (A,B) x (C,D) is built
up as follows:
147
HIGH ACCURACY COMPUTATION
16.
Columns 1-46 of A x C to columns 1-23 of the high order and 1-23 of the low order "ganged"
counters under the special product read-out.
Columns 24-46 of A x D to columns 1-23 of the low order "ganged" counter under the special
carry controls, according as Ax C is positive or negative and plus or minus zero to columns
1-23 of the high order "ganged" counter under the special carry controls and under control
of counter 70.
Columns 24-46 of BxCto columns 1-23 of the low order "ganged" counter under the special
carry controls, according as Ax C is positive or negative and plus or minus zero to columns
1-23 of the high order "ganged" counter under the special carry controls and under control
of counter 70.
Multiply (A,B) by (C,D) and deliver the product to ctrs.
(65,64). Sw. P contains plus zero. Factors may be positive
or negative. Lines where operations may be interposed are
left clear. 7's required if operations are interposed are
given as (7). In general, no quantities should be read into
ctr. 65 before storing the algebraic sign in the choice
counter.
OUT
IN
MISC.
A
761
(7)
C
(7)
871
7
86
87
7
A
761
7
732
732
7
71
732
D
7
P
871
7432
P
871
(7)432
87
7
B
761
(7)
Continued on next page
148
CODING
16. (continued)
OUT
IN | MISC.
C
7
87
E and F.
,.* „ .„ -_w c „„, Known to be positive, columns 24-46 of A x D are read to columns 1-23
„* „ m . n te- t? an d "^unter E remains reset to zero.
A x D is positive or negative.
(b)
17 Multiply (A,B) by (0,D) and deliver the product to (E,F).
"" Sri are positive. Spaces where operations may be
interposed are left clear. 7«s required if operations are
interposed are given as (7).
OUT
IN
MISC.
A
761
(7)
1
D
(?)
F
7
18 Multiply (A,B) by (0,D) and deliver the product to (E ,F).
SwP contains plus zero. Factors may be positive or
negative. Spaces where operations may be inteposed
are left clear. 7's required if operations ^inter-
posed are given as (7). In general no quantities ^should
be read into ctr. F before storing the algebraic sign in
the choice counter.
A
761
1
7
732
732
(7)
D
(7)
Continued on next page
HIGH ACCURACY COMPUTATION
149
18. (continued)
OUT
IN
MISC.
F
7
F
732
7
P
E
7432
(19) When one of the two factors of a product has only 23 decimal places, only two multiplications
need be performed and the factors are of the form (A,B) and (C,0).
(a) If all the numbers are known to be positive:
Columns 1-46 of A x C are read to columns 1-23 of the high order and 1-23 of the low
order "ganged" counters.
Columns 24-46 of B x C are read to columns 1-23 of the low order "ganged" counter.
19. Multiply (A,B) by (C,0) and deliver the product to (69,68).
All values are positive. Lines where operations may be
interposed are left clear. 7's required if operations are
interposed are given as (7).
OUT
IN
MISC.
A
761
(7)
C
(7)
8731
7
86
873
7
B
761
(7)
Continued on next page
150
CODING
19. (continued)
OUT
IN
JY1J.OI/ .
C
(7)
873
7
(b) If some numbers may be negative:
nr>A 1 -01 rvf tho lmi7
uiuci gaii^ci
Columns 24-46 of B x C are read to columns 1-23 of the low order "ganged" counter and
plus or minus zero to the high order "ganged" counter under control of counter 70 ac-
cording as A x C is positive or negative.
20. Multiply (A,B) by (C,0) and deliver the product to (69,68).
cm p contains "lus zero. Factors ma v be oositive or
negative. Lines where operations may be interposed are
left clear. 7's required if operations are interposed are
given as (7). In general, no quantities should be read into
ctr. 69 before storing the algebraic sign in the choice
counter.
OUT
IN
MISC.
A
761
7
732
732
(7)
C
(7)
8731
7
86
873
7
B
761
7
731
732
7
P
8731
432
C
1
i
(7)
i
Continued on next page
151
HIGH ACCURACY COMPUTATION
20. (continued)
OUT
IN
MISC.
873
7
(20) Division in high accuracy computation may be performed by dividing by the high order columns
of the divisor to obtain a first approximation to the reciprocal, iterating once for the reciprocal
and multiplying. Since the operating decimal point lies between columns 23 and 24, division
should be plugged for 24 comparisons and the "Divide N minus Decimal" switch must be set at
zero. If the absolute value of the divisor is such that 1 >|DR| >10" n , in place of 1, 10" n must
be used as the dividend in obtaining the reciprocal. Thus after division the Q-shift counter
stands at zero and the first approximation to the reciprocal is delivered as Q x 10" " . This
quotient is then routed through either the LIO or the SIO counter and shifted to the left.
21. Divide (A,B) by (C,D), where either or both of the quantities may be negative, l>|c| >0.1,
and deliver the quotient to (65, 64). The LIO-OUT is plugged to shift one column to the left.
The SIO-OUTII is plugged to shift positive quantities one column to the left. The SIO-OUTI
is plugged to read the 23rd column of SIO to the first column of the buss.
Sw. P = 1 in the 23rd column.
Sw. Q = 5 in the 2nd column.
Sw. R = minus zero.
Sw. S = 2 in the 23rd column.
Sw. T = 1 in the 1st column.
Counters G, H, 64, 65, 68, 69, 70, LIO and SIO are available for computation but are not
reset.
The equations used in the computation are
V V|c|
N = |(C,D)|
x l = x 0* 2 " N V '
After the iteration, five is added in column 3 to obtain the best result. Errors at various
stages are as follows:
x /10 = 1/10N t 10" 22
-45
-46
x 1 /10 = 1/10N+ 51 x 10
Final result = (A,B)/10(C,D) + 512 x 10'
An additional iteration will gain very little accuracy, the errors then being as follows:
152
CODING
/m _ 1/1 nw j. «> •»■ 1 n~45
)/ iu = i/ lull i vr A xu
Final result » (A,B)/10(C,D) t 32 x 10
-48
The quotient as delivered to (65,64)is (A,B)/10(C,D). (7)'s must be omitted if no operations
are interposed.
|C| to DR
reset ctr. G, reset SIO
reset ctr. H, reset LIO
1 in 23rd col. to DD
reset ctr. 64
reset ctr. 65
reset ctr. 68
reset ctr. 69
reset ctr. 70
18 cycles free for interposed operations
l/(100|C|)toctr. H
i/(iOQJCJ) to SIO
1/(10 |C|) to ctr. G = x /10
-|C| toMC
reset ctr. H
v /Idtn MD
-IcJxq/IO to (69,68)
OUT
IN
MISC.
C
76
72
G
G
7321
H
H
63
P
7
7
7
7
71
71
7
73
73
7
731
731
7
732
732
(7)
H
7
H
874
7
84
G
7
C
761
71
H
H
(7)
VI
8731
7
86
873
7
frvrrHTVi
ia/4 r\n nai
17+ nnn .»
HIGH ACCURACY COMPUTATION
153
21. (continued)
-JD| to MC
-0 to (69,68)
x /10 to MP
2 in 23rd col. to (69,68)
-|D|x /10 to (69,68); (69,68) - (2 - Nx )/10
HO (2 - Nx Q )/10 to MC
X./10 to MP
x Q (2 - Nx Q )/100 to (65,64)
LO (2 - Nx )/10 to MC
C to ctr. 70
5 in 2nd col. to ctr. 64
x /10 to MP
reset ctr. 68
reset ctr. 69
reset ctr. G
OUT
IN
MISC.
D
761
71
R
8731
(7)
G
7
S
8731
(7)
873
7
731
761
(7)
G
(7)
871
7
86
87
7
73
761
7
C
732
7
Q
87
G
7
73
73
7
731
731
7
G
G
7
Continued on next page
154
CODING
zi. (continued;
reset SIO
x Q (2 - Nx )/100 to (65,64)
HO x Q (2 - Nx )/100 to LIO
HO x Q (2 - Nxq)/10 to ctr. G
LO x Q (2 - Nx Q )/100 to SIO
1st col. SIO to ctr. G; reset LIO; G - HO x /10
LO x n (2 - Nx n )/10 to ctr. H; H = LO x,/10
A to MC under control of ctr. 70
reset ctr. 64
reset ctr. 65
HO x 1 /10 to MP
(A,B)x 1 /10to (65,64)
A to MC under control of ctr. 70
LO x /10 to MP
(AjBjx^lO to (65,64)
B to MC under control of ctr. 70
reset ctr. 70
OUi
IN
MISC.
321
87
7
71
765421
7
831
G
7
7
874
7
874
G
763
84
H
7
A
761
7432
7
7
7
71
71
G
(7)
871
7
86
87
7
A
761
(7)432
H
(?)
87
7
B
761
7432
732
i
732
i
7
1
Continued on next page
HIGH ACCURACY COMPUTATION
155
21. (continued)
-HO (A,B)x /10 to ctr. 70
HO x /10 to MP
±0 to (65,64) under control of ctr. 70
±0 to (65,64) under control of ctr. 70
1 in 1st col. to ctr. 64
(A,B)x /10 to (65,64)
OUT
IN
MISC.
71
732
32
G
7
R
871
7432
R
871
7432
T
87
87
7
(21) If 46 column numbers are to be punched in cards, they must be punched in two cards, one con-
taining the high order columns and the algebraic sign, and the second, the low order columns
and the algebraic sign.
22. Punch out the number (A,B).
OUT
IN
MISC.
A
753
51
B
753
75
(22) To print 46 column numbers, the high order columns may be printed on one typewriter and the
low order columns on the other. If the low order columns are printed with several spaces after
the decimal point, the algebraic sign and the decimal point may be cut off and the strips joined
side by side.
23. Print the number (A,B).
OUT
IN
MISC.
A
7432
752
6
B
74321
7521
7
(23) If numbers have been normalized for high accuracy computation, they may usually be printed
with their decimal points in true position by suitable typewriter plugging. See Plugging In-
structions .
(24) The following is an example of the building up of a series in high accuracy computation.
24. Determine Ax 2 + Bx + C, where no information is given of any algebraic sign, store the
result in (E, F), and print it on typewriter I. A, B and C are 46 column numbers stored in
switches (Aj, A 2 ), (Bj, Bg) and (Cj, C 2 ). Sw. P = plus zero, x is stored in ctrs. (xj, Xg).
Counters E, F, 64, 65, 68, 69 and 70 are available for computation. (7)'s must be omitted
if no operations are interposed.
156
CODING
24 . (continued)
A x to MC
reset ctr. 69
reset ctr. 68
x to MP
reset ctr. 70
reset ctr. 65
reset ctr. 64
HO Ax to ctr. 69
"l"l
Aj to MC
AjXj to ctr. 70
+0 to (69,68) under control of ctr. 70
x 2 to MP
±0 to (69,68) under control of ctr. 70
B, to ctr. 69
B« to ctr. 68
Ajx 2 to (69,68)
A 2 to MC
x. to MP
AgXj to (69,68)
x 1 to MC
I
OUT
IN
MISC.
A l
761
7
731
731
7
73
73
x l
7
732
732
7
71
71
7
7
7
8731
7
86
8*73
7
A l
761
7
731
732
7
P
8731
432
x 2
7
P
8731
7432
B.
i
8731
7
B 2
873
873
7
A 2
761
CO
x*
(7)
873
7
I"!
761
7
Continued on next page
157
HIGH ACCURACY COMPUTATION
24. (continued)
reset ctr. 70
HO (Ax + B) to MP
HO (Ax + Bjxj to ctr. 65
LO (Ax + B)x l to ctr. 64
x. to MC
HO (Ax + B)x 1 to ctr. 70
LO (Ax + B) to MP
+ to (65,64) under control of ctr. 70
±0 to (65,64) under control of ctr. 70
(Ax + B)x< to (65,64); turn on typewriter I
x 2 to MC
reset ctr. E
reset ctr. F
HO (Ax + B) to MP
C 1 to ctr. 65
C to ctr. 64
(Ax + B)x to (65,64)
ctr. 65 to ctr. E
ctr. 64 to ctr. F
OUT
IN
MISC.
732
732
(7)
731
(7)
871
7
86
87
7
x l
761
7
71
732
(7)
73
7
P
871
7432
P
871
(7)432
872
87
7
x 2
761
7
E
E
7
F
F
731
7
C l
871
7
C 2
87
(7)
87
7
71
E
7
7
F
7
Continued on next page
158
CODING
O.A /r»nntfTViipri1
print value in ctr. 65 on typewriter I
print value in ctr. 64 on typewriter I
OUT
IN
MISC.
71
7432
752
6
7
7432
752
6
159
NORMALIZING REGISTER
(1) Any positive quantity may be shifted so that its first significant digit stands in the 23rd machine
column. This is done within the machine by multiplying the given quantity by a one in such a
position that the first significant digit will fall in the 23rd column of the PQ counter. The prod-
uct is then read out of the first 23 columns of the PQ counter by means of the low order product
read-out (86 in the Out column). The number of columns shifted is recorded in a counter and a
predetermined number of significant digits and a power of ten are read out. For example, if
0000 35296 73145 89740 28715
0000 00000 00000 27557 68214
stand in the machine, operating with decimal point between columns 15 and 16, they may be read
out as
3529 1 ; i.e., 3529 x 10
2755 -9 ; i.e., 2755 x 10~9.
Thus the second quantity printed indicates the power of ten by which the first quantity is to be
multiplied.
(2) The number of significant digits printed and the position of the decimal point, if printed, are
determined by the typewriter plugging.
(3) The power of ten recorded is determined by the position of the final decimal point and the oper-
ating decimal point of the machine .
A constant K is placed in a switch in columns 20 and 21. Here K = 23 - n - d, where d is
equal to the number of digits to the left of the final decimal point and the operating decimal
point of the machine lies between columns n and n + 1 .
The power of ten recorded lies in columns 20 and 21 and must be read out or printed out of
those columns.
(4) Negative quantities must be routed through this procedure as positive absolute values. The al-
gebraic sign is stored in counter 70 and the final read-out of the quantity must be under control
of counter 70.
(5) The code 8321 in the In column shifts the quantity under consideration into the first 23 columns
of PQ. The code 8321 in the Out column reads the amount of the shift to the counter indicated.
These codes are not independent and must be used in conjunction with the multiplication coding
as shown below.
(6) The special coding requires nine cycles of computation time. Counter A contains the quantity
to be treated. Counters B, C, D and E are reset and available for computation. Switch SC con-
tains the constant K. At the end of the process, counter B contains the power of ten, counter D
contains the quantity under consideration with its first significant digit in the 23rd column and
counter E contains the "one " multiplier selected by the shift circuit. Note that the line of coding
reading the normal product-out may not be used for any other operation.
1. The operating decimal point lies between cols. 15 and 16.
The final decimal point is to lie between cols. 19 and 20.
Thus K = 4 is placed in col. 20 of sw.SC. The quantity in
ctr.A is shifted and printed together with its power of ten.
OUT
IN
MISC.
A
761
7
SC
B
7
Continued on next page
160
CODING
1. (continued)
This line of coding may contain any of the codes normally
interposed in multiplication. (A second such line may also
be interposed if it is known that the quantity to be shifted
does not equal zero.)
OUT
IN
MISC.
A
8321
E
7
8321
C
7
7
C
B
32
7
86
D
7
D
7432
752
6
B
7432
752
7
(7) It is advisable to check the multiplication involved in this process by interchanging ™fW™
and multiplicand. Thus the "one" multiplier, read into storage counter E, is used as the multi-
pTfca^in the second multiplication. The product is again read out under the special low order
read-out.
2. The operating decimal point lies between cols. 15 and
16. The final decimal point is to lie between cols. 19
and 20. The tolerance of one in the first column lies
in sw. SB.
KJVl
in
IVilOV-r . t
A
761
7
SC
B
7
A
8321
E
7
8321
C
7
7
1 —
C
B
1
32
7
86
D
7
E
761
7
74
74
7
SB
74
Continued on next page
NORMALIZING REGISTER
161
2. (continued)
OUT
IN
MISC.
A
7
D
F
(7)32
7
86
F
7
F
74
71
64
162
LOGARITHM UNIT
(1) The logarithmic function delivered bv the machine is log* ~x. Logarithms to other bases may
* ' " » w lu " "
be obtained bv multiDlvine bv a suitable constant.
log a N =
lQ glQ N
log 10 a
= log 1() N . log a 10
In particular
log e N = log 1Q N • log e 10
where
log e 10 = 2.302 585 092 994 045 684 017 991.
(2) If the operating decimal point lies between columns 21 and 22, the error in this function is less
than 5 x 10-21. If the decimal point lies between columns n and n + 1, n< 21, the error is
less than 10~ n + 5 x 10 -ai . If desired, for log x > 0, a coded half pick-up may be added and the
error reduced to l/2(10 _n + 10-20) as shown in example 4 below.
(3) The range of arguments covered is 10-22 to 1023 _ l.
(4) Logarithms with negative characteristics may not be computed directly if there are ten or
fewer operating decimal places. For exception, see note (10).
(5) The two dial switches labeled "Log N value" to the right of the sequence mechanism must be
set at 22 - n, where the operating decimal point is between columns n and n + 1 .
(6) The logarithm unit requires plugging of the LIO counter to care for the decimal point. See
Dliirrmrtn 1 Tncf-riiAfiAnc
(7) The LIO counter may be used as a storage counter, for the addition of positive quantities, and
to shift numbers, since it has a pluggable read-out. See Logarithm In-Out Counter and Plug-
ging Instructions.
(8) Before using the logarithm unit it should be tested on known values:
e = 2.718 281 828 459 045 235 360 287,
log,„e = 0.434 294 481 903 251 827 651 129 .
JLU
(9) Any operation not using the buss may be carried on during the logarithm computation time.
This requires a 7 in the Miscellaneous column of the first line of logarithm coding and no
automatic (no 7 in the Miscellaneous column) in the last line of interposed coding. This coding
is shown in example 5.
1. x lies in sw. or ctr. A. Determine log lf) x and deliver it
to ctr. B.
OUT
IN -
MISC.
A
762
831
B
n
•
...
763
1
LOGARITHM UNIT
163
2. x lies in sw. or ctr. A. Determine log in |x| and deliver
it to ctr. B. 1U
3. x lies in sw. or ctr. A. Determine log x and deliver it
to ctr. B. Log e 10 lies in sw. P.
Log x =»0. x lies in sw. or ctr. A. Determine log 1f) x and
deliver it to ctr. B. If the operating decimal point lies
between columns n and n + 1 , sw. P must contain a 5 in
the (21 - n)th column.
5.
Print the quantities in ctrs. C and D. Punch the quantity
in ctr. E. Step the value tape on interpolator I ahead
twice, x lies in sw. or ctr. A. Determine log.. n x and
deliver it to ctr. B.
(repeat this line 23 times)
OUT
IN
MISC.
A
762
2
831
B
7
763
A
762
831
B
7
763
B
761
P
7
B
B
B
7
A
762
P
765421
7
831
B
7
763
C
7432
D
74321
E
753
A
762
75
752
753
753
7
7521
831
B
7
•
763
164
CODING
(10) If negative logarithms are computed when there are ten or fewer operating decimal places,
more nines will be required for the read-out of the complementary figure than the ten that
are available by plugging. The additional nines required may be supplied from a switch under
control of the choice counter. If the operating decimal point is between columns 8 and 9, 13
nines are needed in columns 11-23. Ten of them are supplied by plugging to ten columns, say
14-23, and three are supplied from a switch to columns 11-13.
6, The operating decimal point lies between cols. 8 and 9.
x lies in sw. or ctr. A. Sw. P has 000 in cols. 1.1-13.
The other columns of sw. P (cols. 1-10 and 14-24) are
set on the blank position (not zero). Nines are plugged
to cols. 14-23. The algebriac sign, col. 24, is bottle-
plugged as usual. Determine log x and deliver it to
ctr.B. 10
OUT
IN
MISC.
A
762
831
B
7
B
732
763
P
B
IlVN
165
EXPONENTIAL UNIT
(1) The exponential function delivered by the machine is 10*. Exponential functions of other bases
may be obtained by multiplication.
a X . 10 X log 10 a
In particular
e X = 10 X 1Og 10 e
where
log 1() e - 0.434 294 481 903 251 827 651 129,
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
If the operating decimal point lies between columns 21 and 22, the error in this function is less
than 5 x 10 «*. If the decimal point lies between columns n and n + 1, n < 21, the error is
less than 10~n + 5 x 10-21. A half pick-up maybe added and the error reduced, as shown in ex-
ample 5 below, to l/2(10~ n + lO" 20 ).
The range of arguments covered is - 20 to 23 - lQ-« where the operating decimal point lies
between columns n and n + 1 .
Any operation not using the buss may be carried on during the exponential computation time
This requires a 7 in the Miscellaneous column of the first line of exponential coding and no'
automatic (no 7 in the Miscellaneous column) in the last line of interposed coding. This is shown
in example 6.
The exponential unit requires plugging of the EIO counter to care for the decimal point See
Plugging Instructions.
H an exponential is preceded by a multiplication or a division, at least one line of coding (blank,
blank, 7) or some other operation not involving a functional unit must be inserted between the
operations .
If an exponential is preceded by an interpolation, at least one line of coding (blank, blank 7) or
some other operation not involving a functional unit must be inserted between the operations
This with the last line of interpolation coding makes two such lines intervening.
The hyperbolic functions may be obtained from the exponential functions by algebraic oper-
ations, j » r
Before using the exponential unit in a computation, it should be tested on known values.
10 log 10 e
log 10
* e
e = 0.434 294 481 903 251 827 651 129
e = 2.718 281 828 459 045 235 360 287
1. x lies in sw. or ctr. A. Compute 10* and deliver
it to ctr. B.
OUT
IN
MISC.
A
7621
741
832
B
731
166
CODING
2. x lies in sw. (except IVS) or ctr. A. Compute 10"
and deliver it to ctr. B.
3. x lies in IVS. Compute 10" x and deliver it to ctr. B.
5.
6.
4. x lies in sw. or ctr. A. Ctr. C is available for compu-
tation. Log 1fl e lies in sw. P. Compute e x and deliver
it to ctr. B.
x lies in sw. or ctr. A. Sw. P contains a 5 in the
(21 - n)th column, where the operating decimal point
lies between columns n and n + 1 . Compute lO*
and deliver it to ctr. B.
Print the quantities in ctrs. C and D. Punch the quantity
in ctr. E. Step the tape on interpolator II back three
times, x lies in ctr. A. Compute lO* and deliver it to
ctr.B.
OUT
IN
MISC.
A
7621
32
741
832
B
731
8431
7621
21
741
832
B
731
A
761
P
C
7
17
i :
C
7621
741
832
B
731
A
7621
741
P
741
832
B
731
C
7432
Continued on next page
EXPONENTIAL UNIT
167
6. (continued)
(repeat this line 22 times)
7.
x lies in sw. or ctr. A. Ctr. C is available for compu-
tation. Sw. P = 1 . Sw. Q = 1/2 . Sw. R = log, e.
Compute sinh x and deliver it to ctr. B. If x Is known
to be positive, bracketed codes and lines may be omitted.
OUT
IN
MISC.
D
74321
E
753
A
7621
75
752
7541
7541
7
7521
541
741
832
B
731
A
761
(2)
R
C
7
7
C
7621
741
832
B
731
B
76
32
P
B
7
B
761
(7)
(732)
(732)
(7)
(A)
(732)
(7)
Q
7(432)
B
B
B
7
168
CODING
8. x lies in sw. or etr, A. Ctr. C is available for compu-
tation. Sw. P = 1. Sw. Q = 1/2. Sw. R = log in e. Com-
pute cosh x and deliver it to ctr. B.
9. x lies in sw. or ctr. A. Sw. P = 1 . Sw. Q = log 1Q e .
Ctrs. C and D are available for computation. Compute
tanh x and deliver it to ctr. B. If x is known to be posi-
tive, bracketed codes and lines may be omitted.
OUT
IN
MISC.
A
761
R
C
7
7
C
7621
2
741
832
B
731
B
76
P
B
7
B
761
Q
7
B
B
B
7
A
C
7(2)
A
C
7(2)
C
761
IT7\
(732)
|
(732)
(7)
(A)
(732)
(7)
Q
D
7
7
D
7621
741
832
B
Continued on next page
EXPONENTIAL UNIT
169
9. (continued)
OUT
IN
MISC.
731
P
B
7
B
76
7(432)
P
B
732
P
B
32
B
7
B
B
B
7
170
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
'1* Roots and reci"rocals of roots ma" be found by using logarithms and exponentials. However,
if a "ood first approximation is available ? the method of iteration is not only faster, but is also
self -corrective.
(2) Square roots may be found using logarithms and exponentials by
1/2 m 10 (log 10 N)/2
1. N lies in ctr. A. N 1 / 2 is to be delivered to ctr. B. Ctrs.
C and D are available for computation. Sw. P = 1/2.
OUT
IN
MISC.
A
762
831
C
7
763
C
761
P
D
7
7
D
7621
741
832
B
731
(3) The Newton-Raphson method of determining the roots of an equation f(x) = requires that
f'(x) £ and f "(x) f between the first approximation, x_, to the root of f(x) and x, the root
sought, and that f(x n ) • f "(xj * 0. Then
(A) x„
1 n
*0' v
f(x n )
f'(«n>
n = 0,1,2, ...
gives successive approximations to x. If successive iterations involving division are performed,
4-VkA 4aaiii*qait rvf sliTrio-irtri cVtrviilsl lr%a cnAAcicciTralir ins»i*£}QCQiHI TTi-i o mo£Tir*H mow o-f4*Qi* ■fiiT'f Viqt* in_
vestigation be applied in some cases when the function does not satisfy all of the above con-
ditions .
In some cases the computation may be simplified by using
*(*n>
(B) x =x , n = 0, 1,2, ...
n+1 n f'(x Q )
for the successive iterations, though this does not converge as rapidly as (A).
(4) If the method of iteration is used to obtain the positive square root of N, then
x « = fa.. + n fx \ /2
~n + j. r ~u " -'--ri" -
171
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
In performing the successive iterations, the accuracy of division should be successively in-
creased. The error, e n + i> of x n + i is given by:
e n + 1 = x n + 1
N l/2
= e ^ /2(e n + N 1/2 ) and
'n+ 1
: e 2 /2N
n
1/2
0.
(5)
(6)
Since most machine computation is repeated for values of N which change by small amounts,
the root or reciprocal calculated for the preceding value of N will in general be available for
use as a first approximation when starting the next iterative process.
2. N lies in ctr. A. The approximation to N ™ lies in ctr. B.
Read the next approximation to ctr. B. Sw. P = 1/2.
OUT
IN
MISC.
B
76
A
B
7
B
761
P
7
B
B
B
7
If two successive iterations are to be made in finding N 1 / 2 , machine time may be saved by
using the following coding which involves two divisions, one multiplication and four additions
instead of two divisions and two multiplications. Usually it will be possible to interpose the
four adding cycles, thus reducing the time for two iterations to 81 cycles.
3. N lies in ctr. A. The approximation Xq to N 1 / 2 lies in ctr. B. Read the approximation
x 2 to ctr. B. Sw. P = 1/4. (7)'s are to be omitted if no operations are interposed. Ctr.C
is available for computation.
x Q to MC
reset ctr. C
x Q to ctr. C
1/4 to MP
x to ctr. C
Xq to ctr. C
OUT
IN
MISC.
B
761
7
C
C
7
B
C
P
7
B
C
7
B
C
7
Continued on next page
172
CODING
3 /c.nntiTHie>d\
... \— — — ~ /
x Q to ctr. C; C = 4x
reset ctr. B
x~/4 to ctr. B
4x to DR; place limitation
reset ctr. C
Nto DD
n + 1 cycles free for interposed operations where n is
the number of significant digits (including the first. "no
go") for which the Misc. 6432 code is plugged.
N/4x Q to ctr. B; B = x Q /4 + N/4x q = Xj /2
x /2 to ctr. C
x t /2 to ctr. C
x./2 to ctr. C
x /2 to ctr. C; C = 2x
2x l to DR
NtoDD
n + 1 cycles free for interposed operations where n is
the number of significant digits (including the first "no
go") in the quotient.
N/2x t to ctr. B; B = Xj/2 + N/2x t = x g
OUT |
IN |
MISC.
B
C
7
B
B
B
7
C
76
76432
C
C
(7)
A
(7)
B
7
B
C
7
B
C
7
B
C
7
B
C
7
C
76
(7)
A
(7)
B
1
7
(7) If other computations are being carried on in which operations may be interposed, the time
for three successive iterations may be reduced from three divisions and three multiplications
to three divisions, one multiplication and 13 adding cycles, which may be interposed.
(8) To find the cube root of N by iteration
.2
x n «• 1 - 2 V 3 + N/3x n
and
e ^e^e + N 1/3 ).
n+ 1* n' v n
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
173
4. N lies in ctr. A. The approximation to N ' lies in
ctr. B. Read the next approximation to ctr. B. Ctr. C
is available for computation and sw. P = 1/3. (7)'s
must be omitted if no operations are interposed.
n cycles free for interposed operations where n is the
number of significant digits (including the first "no go")
in the quotient.
(9) The cube root of N may also be found by iteration by
3
*n+l
x n + 2N
2x n ° + N
OUT
IN
MISC.
B
761
7
C
C
(7)
B
(7)
C
7
C
76
7
C
C
7
B
C
A
7
B
C
(7)
C
7
C
761
7
C
C
7
B
B
P
(7)
B
7
....
*n
174
CODING
This involves tnree multiplications ana a envision uiu in most eases converges i*iuv,« »»»'»■
rapidly than the method given in note (8), so that fewer iterations need be used for the «esire~
accuracy. If two successive approximations x n and x n + i agree in the first i significant digits,
then x n + i will be correct to 3i - 2 digits. The error e n + l is given by:
e n< e n + 2N }
e n + 1 ~ t /3 3
2(e n + N 1/iJ ) + N
5. N lies in ctr. A. The approximation to N ' lies in
ctr. B. Read the next approximation to ctr. B. Ctrs.
C and D are available for computation, (7)'s must be
omitted if no operations are interposed.
Ctr.C =x
Ctr.D =2x n +N
Ctr.C = x +2N
OUT
IN
MISC.
B
761
7
C
C
7
D
D
B
(7)
C
7
C
761
7
C
C
7
A
D
!
B
(7) !
1
C
7
C
D
7
c
D
7
D
76
7
A
C
7
A
C
C
7
C
C
7
Continued on next page
175
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
5. (continued)
n - 1 cycles free for interposed operations where n is the num-
ber of significant digits (including the first "no go") in the
quotient.
Ctr.C =(x Q 3 + 2N)/(2x Q 3 + N)
Ctr. B = x o (x o 3 + 2N) / (2x Q 3 + N) = Xj
(10) The reciprocal of N may be found by iteration using
x = x (2 - Nx ) ,
n + 1 n x n 7 '
e 1 = -Ne
n + 1 n
OUT
IN
MISC.
D
D
(7)
C
7
C
761
(7)
B
7
B
B
7
C
C
(7)
B
7
In high accuracy computation, it is necessary to use this process for division.
6. N lies in ctr. A. The approximation to 1/N lies in ctr. B.
Ctr. C is available for computation. Sw. P =2. (7)'s
must be omitted if no operations are interposed. The new
approximation to the reciprocal of N is to be delivered
to ctr.B.
OUT
IN
MISC .
A
761
732
C
C
7
P
C
B
(7)
Continued on next page
176
CODING
u. ^ummucGj
rump
TXT
MISC .
c
7
B
761
(7)
C
7
C
C
7
B
B
B
7
(11) In many applications of the process of iteration the choice of the function f(x) can be so made
as to conserve much machine time. This is evident in iterating for 1/nVp. f(x) may be written
either as
(1) f(x) = l/x P - N
or (2) f(x) = 1 - NxP .
(1) leads to
< la > x n + l =x
r
»!'
xt n 1
which requires p + 2 multiplications, unless N/p is available, in which case only p + 1 multi-
plications are required.
(2) leads to
(2a) x
1 + (p - l)Nxj
n + 1
pNx n
(P-D
which requires p + 1 multiplications and a division. Obviously, the former requires less ma-
chine time than the latter and should be used for all roots of reciprocals. If (la) is used to
obtain 1/N*/*, the error after each iteration is
3e n "N'
7. N lies in ctr. A. The approximation to N"
1/2
lies in ctr.
B, Read the next approximation to ctr, B. Ctr. C is avail-
able for computation. Sw. P = 1/2. Sw. Q =3. (7)'s must
be omitted if no operations are interposed.
OUT
IN
MISC.
B
761
7
C
C
(7)
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
177
7. (continued)
OUT
IN
MISC.
B
(7)
C
7
C
761
732
C
C
7
Q
C
A
(7)
C
7
C
761
7
C
C
(7)
B
(7)
C
7
C
761
7
C
C
(7)
P
7
Continued on next page
178
CODING
7 . (continued)
8.
-1/2
N/2 lies in ctr. A. The approximation to N ' lies
in ctr. B. Read the next approximation to ctr. B. Ctr.
C is available for computation. Sw. P = 3/2. (7)'s
must be omitted if no operations are interposed. The
computation of example 7 may be modified so that the
— ^i-i j ~r ^^r>w>y-.io Q moTi ho napH fnr oaph .Qiir.p.pssive
jl-^-ii-j, a ri OT , tf>A. first, tb^f^b" reouiring four mul-
tiplications for the first iteration and three for each
thereafter. In this case, Sw. Q = 3/2, and N/2 is com-
puted directly and retained, rather than computing each
iteration in the form
x < = x (3/2 - x * N/2) a
n + 1 n v ' n
OUT
IN
MISC.
B
B
B
7
B
761
7
C
C
(7)
B
(T)
C
7
C
761
7
C
C
7
P
C
A
(7)32
1
C
7
C
761
(7)
B
7
c
C
i
7
_L, .„ 1
Continued on next page
179
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
8. (continued)
OUT
IN
MISC.
B
B
(V)
B
7
(12) The Rule of False Position
If f(x) is continuous in the interval a< x< b and f(a) and f(b) are of opposite sign, then
(b - a) f (a)
a' = a
f(b) - f (a)
is a first approximation to the root of f(x) lying between a and b. Since f(a') and either f(a)
or f(b) are of opposite sign, either
„ (a 1 - a) f(a) „ ^
a" = a - i L—LJ- or a" = b -
„ _ u (a- - b) f(b)
f(a') - f(a)
is a second approximation.
f(a') - f(b)
9. If counter A = a
counter B = b
counter C - f(a)
counter D = f(b)
switch P = 1/2
and counters E through L and counter 70 are available for computation, the following coding will
deliver: & &
a or b depending on the sign of f(a') to counter A,
a 1 to counter B,
f(a) or f(b) depending on the sign of f(a') to counter C,
f(a') to counter D.
The coding may be repeated to obtain the desired accuracy and the accuracy of division should
be increased with the repetitions .
reset ctr. F.
a to ctr. F
- b to ctr. F; F =a - b
f(a) to MC
reset ctr. I
OUT
IN
MISC.
F
F
7
A
F
7
B
F
732
C
761
7
I
I
7
Continued on next page
180
CODING
9 . (continued;
f(a) toctr.I
- (b - a) to MP
-f(b) toctr.I; I =f(a)-f(b)
reset ctr. 70
reset ctr. K
- (b - a)f(a)toetr.K
f(b) - f(a) to DR
reset ctr, E
4-„ „*■». TP
- (b - a) f(a) to DD
reset ctr. K
a to ctr. K
b to ctr. E; E = a + b
reset ctr . H
f(a) to ctr. H
f(b) to ctr. H; H = f(a) + f(b)
reset ctr. G
f(a) to ctr. 70
(a - b) or - (a - b) to ctr. G
reset ctr. J
[f(a) - f(b)] or - [f(a) - f(b)] to ctr. J
a' in ctr. K
f(a') is computed and stored in ctr. L; during the compu-
tation, ctr. 70 is reset
- f(a') to ctr. 70
2a or 2b to ctr. E under control of ctr. 70
OUT
IN
MISC.
C
I
F
7
D
I
732
732
732
7
K
K
K
7
I
76
732
E
E
7
1
A
E
K
7
K
K
7
A
K
7
B
E
7
H
H
7
C
H
|
7
I |
D
H
i
7
G
G
1
C
732
7
F
G
7432
i
»
7
I
J
432
K
7
732
732
7
L
732
732
G
E
7432
Continued on next page
SQUARE ROOTS AND OTHER ITERATIVE PROCESSES
181
9. (continued)
2f(a) or 2f(b) to ctr. H under control of ctr. 70
2a or 2b to MC
reset ctr. B
a' to ctr. B
1/2 to MP
reset ctr . D
f(a') to ctr. D
reset ctr. A
a or b to ctr. A
2f (a) or 2f(b) to MC
1/2 to MP
reset ctr. C
f(a) or f(b) to ctr. C
OUT
IN
MISC.
J
H
7432
E
761
7
B
B
7
K
B
7
P
7
D
D
7
L
D
7
A
A
A
7
H
761
(7)
p..
7
C
C
C
7
182
SINE UNIT
(1) If the operating decimal point lies between columns 22 and 23, the error in this function is xess
than 5 x i0~". If the decimal point lies between columns n and n + I, n< 22. the error is
less than 6.5 x 10-n + 5 x 10-22. A half pick-up may be added and the error reduced to less
than 6 x 10 _n + 5 x 10~ 22 as shown in example 5 below.
(2) Any positive or negative argument in radians may be used, except that sines of third and fourth
quadrant angles cannot be computed directly if there are eleven or fewer operating decimal
places. For exception, see note (10).
(3) The sine unit requires plugging of the SIO counter and the read-out of 1/2 ir to care for the
decimal point. See Plugging Instructions.
(4) The SIO counter may be used as a storage counter, for the addition of positive quantities and to
shift or split numbers, since it has pluggable read-in and read-outs. See Sine In-Out Counter
and Plugging Instructions.
(5) Before using the sine unit in a computation it should be tested on known values.
sin 0.584 073 464 102 067 615 3736 = 0.551 426 681 241 690 550 6611
sin 1.867 258 771 281 654 092 2989 = 0.956 375 928 404 503 013 4325
sin r = sin 3.141 592 653 589 793 238 4626 = -
sin 3.867 258 771 281 654 092 2989 =-0.663 633 884 212 967 502 1510
sin 4.867 258 771 281 654 092 2989 =-0.988 031 624 092 861 789 9878
The unit should also be tested for sines of negative arguments.
(6) Any operation not using the buss may be carried on during the sine computation time. This
requires a 7 in the Miscellaneous column of the first line of sine coding and no automatic (no 7
in the Miscellaneous column) in the last line of interposed coding. This is shown in example 6
below.
(7) Two sines may not be computed successively. At least one line of coding, (blank, blank, 7) or
some other operation not involving the functional units must be inserted.
(8) The cosine may be computed by the sine unit by means of the relation
cos x = sin( v/2 - x).
(9) The remaining trigonometric functions may be computed by the usual algebraic operations.
1. x lies in sw. or ctr. A. Compute sin x and deliver it
to ctr. B.
OUT
IN
MISC.
A
7631
84
B
7
7321
SINE UNIT
183
2. x lies in sw. (except IVS) or ctr. A. Compute sin (-x)
and deliver it to ctr. B.
3. x lies in IVS. Compute sin (-x) and deliver it to ctr. B.
4. x lies in sw. or ctr. A. irft. lies in sw. P. Ctr. C
is available for computation. Compute cos x and
deliver it to ctr. B.
5. x lies in sw. or ctr. A. Compute sin x and deliver it
to ctr. B. Sw. P contains a 5 in the (22 - n)th column
when the operating decimal point lies between columns
n and n + 1 .
6. Print the quantities in ctrs. C and D. Punch the
quantity in ctr. E. Step the value tape on interpo-
lator IE back twice, x lies in sw. or ctr. A. Compute
sin x and deliver it to ctr. B.
(repeat this line 23 times)
OUT
IN
MISC.
A
7631
32
84
B
7
7321
8431
7631
21
84
B
7
7321
P
C
7
A
C
732
C
7631
84
B
7
7321
A
7631
P
874
7
84
B
7
7321
C
7432
D
74321
E
753
A
7631
75
752
7542
7
7521
542
Continued on next page
184
CODING
OUT
IN
MISC S
84
B
7
7321
(10) If negative sines are computed when there are eleven or fewer operating decimal places, more
nines will be required for the read-out of the complementary figure than the ten that are avail-
able by plugging. The additional nines required may be supplied from a switch under control of
the choice counter. If the operating decimal point is between columns 9 and 10, 13 nines are
needed in columns 11-23. Ten of them are supplied by plugging to ten columns, say 14-23, and
three are supplied from a switch to columns 11-23.
7. The operating decimal point lies between cols. 9 and 10.
x lies in sw. or ctr a A-. Sw= P has 000 in cols, 11-13,
The other columns of sw. P (cols. 1-10 and 14-24) are
set on the blank position (not zero). Nines are plugged
to cols. 14-23. The algebraic sign, col. 24, is bottle-
plugged as usual. Compute sin x and deliver it to ctr. B.
OUT
IN
MISC.
A
7631
84
B
7
B
732
7321
P
B
7432
(11) Before using the sine unit, the "85-1 P.U." switch and "SIO-OUT-2 Invert Control" switch must
both lie in the on position.
185
INTERPOLATORS
(1) If an interpolator has not been in use for some time, it should be tested before being used in a
computation. Diagonal numbers should be read out. If interpolation is to be carried on, several
values should be computed.
(2) A tape containing a set of numerical values, arbitrary constants or random values of a function
is called a value tape rather than a functional tape.
(3) Before using a functional tape, two switch settings must be made. One half the number of argu-
ments is set up in the push button switches labeled "Value Tape set up 1/2 "A" values in tape"
above the interpolator. The number of interpolational coefficients (including Cq) is set in each
of the dial switches labeled "Set up number of "C" values on each switch" above the interpo-
lator. See note (28) for special use of the dial switches.
(4) The tape decimal point, the "highest order 'h' " and the interval of the argument must be speci-
fied for proper plugging of the interpolators. If the tape contains negative C values, the decimal
point may not be shifted to the right. See Plugging Instructions.
(5) It is desirable that functional tapes be designed with the tape decimal point between columns 15
and 16 unless more decimal places are needed for the desired accuracy.
(6) A functional tape positions to the closest value of the argument if the Miscellaneous column of
the first line of interpolation coding is blank or 61 . It positions to the closest lower value of
the argument if the Miscellaneous column of the first line of coding contains 641 or if the first
column of the interpolation counter is not plugged.
(7) If an argument which is not in the range of the tape is sent to the interpolator, a red light is
switched on above interpolator I and the machine is stopped.
(8) Interpolators I, II and III are distinguished by the operational codes 7654, 76541 and 76542 re-
spectively in the In column.
1.
x lies in sw. or ctr. A. The functional tape is on interpo-
lator I. Determine f(x) and deliver it to ctr. B.
2.
x lies in sw. (except IVS) or ctr. A. The functional tape
is on interpolator II. Determine f(-x) and deliver it to
ctr.B.
OUT
IN
MISC .
A
7654
62
841
A
763
B
73
7
A
76541
32
62
841
A
763
32
Continued on next page
186
CODING
(continued j
out*
TXT
hi
MISC.
B
73
7
3. x lies in ctr. A. The functional tape is on interpolator III.
Determine f(lx|) and deliver it to ctr. B.
A
76542
2
62
841
A
763
2
B
73
7
(9)
(10)
An addition, reset, reading to a print counter or any other operation not involving the multiply-
divide unit or the interpolators may be inserted in the last line of interpolation coding. The
typewriters may be turned on or off in the next to the last line of interpolation coding (line re-
setting the interpolation check counter).
4. x lies in ctr. A. The functional tape is on interpolator I.
Determine f(-|x|) and deliver it to ctr. B. Reset ctr. C
in the last line. Turn off typewriter II.
OUT
IN
MISC.
A
7654
1
I
62
841
A
763
1
8731
B
73
C
C
7
Occasionally when the interpolator positioning time is very short (the same or the next argu-
ment) it may be desirable to use the computation time to cover one or more prints. The quantity
to be printed must be read to the print counter before the interpolation is initiated as shown
below.
5. Print the quantity in ctr. C on typewriter I during compu-
tation time, x lies in ctr. A. The functional tape is on
interpolator II. Determine f(x) and deliver it to ctr. B.
OUT
IN
MISC.
C
7432
A
76541
62
841
A
763
7
Continued on next page
187
INTERPOLATORS
5 . (continued)
OUT
IN
MISC.
752
B
73
7
6. Print the quantities in ctrs. C and D on typewriters I and
II. x lies in ctr. A. The functional tape is on interpo-
lator IE. Determine f(x) and deliver it to ctr. B.
c
7432
D
74321
752 '
7
A
76542
62
841
A
763
7
7
Repeat this line (blank,
blank, 7) a sufficient num-
ber of times so that the
positioning time plus
these lines cover 23
cycles.
7
7521
B
73
7
(11) It may be desirable to carry on calculations not involving the interpolators after interpolation
is initiated and during tape positioning time. In this case sufficient cycles must be inserted to
cover more than the maximum tape positioning time of the given problem. The maximum tape
positioning time for interpolation of order k is
P = 8 + N(k + 2)/2
where
N = the number of arguments to be covered
k + 1 = the number of interpolational coefficients including C .
(12) If operations are inserted during tape positioning time, the read-in of the argument to the in-
terpolator in the first line of coding may not be altered by any operational code such as the
invert code.
188
CODING
7. x lies in sw. or ctr. A. The functional tape is on interpo-
lator I. Determine f(x) and deliver it to ctr. B. Insert
other operations during tape positioning time .
OUT
IN
MISC .
A
7654
61
762
Other computations in-
serted here must cover
tape positioning time.
841
7654
A
763
B
73
7
x lies in sw. or ctr. A. Ctr. C is available for compu-
tation. The functional tape is on interpolator II. Deter-
mine f(-x) and deliver it to ctr. B. Insert other oper-
ations during tape positioning time .
A
C
732
C
76541
61
762
Other computations in-
serted here must cover
tape positioning time.
841
76541
C
763
B
73
7
(13) If operations are inserted during tape positioning time, a 641 code in the Miscellaneous column
will insure that the tape will position to the closest lower value of the argument rather than to
the closest value of the argument. The positioning of the tape to the closest lower value may
Ink** iica/1 frw 0£kl*a/*+ /iofo oc in r»OY»r\ rwiHIoT* intornoloHnn
9. A tape is punched xj., f(xi), X2, f(x2), ... . x lies in sw.
or ctr. A. It is required to determine f(x n ) where
XjjS x< x n + i and deliver it to ctr. B. Insert other
operations during tape positioning time. The tape is
on interpolator I.
OUT
IN
MISC.
A
7654
641
762
Other computations in-
serted here must cover
tape positioning time.
73
85
753
B
7
189
INTERPOLATORS
(14) A tape designed for an odd function need only be punched for positive values of the argument
and counter 70 may be used to determine the sign of the result.
10. A tape for f(x) = - f(-x) is on interpolator II. x lies in
ctr. A. It is required to determine f(x) and deliver it
to ctr. B. Ctrs. 70 and C are reset and available for use.
OUT
IN
MISC.
A
732
7
A
76541
2
62
841
A
763
2
C
73
C
B
7432
(15) All functional tapes and value tapes should be checked as described in the section on the design
of functional tapes before being used in a computation.
(16) No switch setting or plugging is required for the use of a value tape since the values are read
directly into the buss. If the decimal point of a value tape is not the same as the operating
decimal point of the machine, the values must be routed through either the LIO or SIO counter
to shift them to the proper position.
(17) Selected coefficients may be read out of a functional tape as if it were a value tape. The argu-
ments cannot be read out because of the argument code punched in the first column.
(18) Since the sequence control tape may contain coding to step the interpolators ahead or back and
to read values from the tape, the value tape must be synchronized with the control tape. There-
fore, the starting position of a value tape must be clearly indicated.
(19) The codes selecting the interpolator from which values are to be read are 85, 851 and 852 in
the Out column for interpolators I, II and HI respectively.
(20) The codes stepping the interpolators ahead are 753, 7531 and 7532 in the Miscellaneous column
for interpolators I, II and HI respectively.
(21) The codes stepping the interpolators back are 754, 7541 and 7542 in the Miscellaneous column
for interpolators I, II and HI respectively.
11. Step interpolator I ahead.
OUT
IN
MISC.
753
12. Step interpolator n back.
7541
13. Read the value from interpolator HI to ctr. B.
852
7
B
7
190
CODING
14. Step interpolator I ahead and read the value to ctr. A.
OUT
IN
MISC.
85
753
A
7
15. Step interpolator II back and read the value to ctr. A.
851
7541
A
7
16. Read the value from interpolator m to ctr. A, and step
ahead.
852
7
A
7532
85
7
A
754
17. Read the value from interpolator I to ctr. A, and step
back.
(22) If it is desired to read successive values, n + 1 cycles are necessary to read out n values.
18, Read five successive values from a tape on interpolator II,
supposing the tape to be standing on the first value, to ctrs.
A, B, C, D and E, and step the tape to the next value.
OUT
IN
MISC.
851
7
851
A
7531
851
B
7531
851
C
7531
851
D
7531
E
7531
/nn\ a x j.- ±l—\ „.._u r,„ n ^.„— ;^,- nt mM<c<f>m^ -Jo rvnr>/»Vio/i in q tana mhoro n ic tho nnmhor nf
\40) /I lUUCUUU J-V* 1 / » °^^ U I a OCX ICO V/A OUUOlcUlbU, 1.VJ JJUUV,uvu ».** ~ —.^^ ., ~~.~ .. — ~~ ..—.~-w. _-
the entry in the tape. The following examples illustrate the selection of data from such a tape.
19. Assuming the tape is on interpolator ni and standing on
f(n), read f(n - 2), 2f(n), f(n + 1), f(n + 2) to ctrs. A, B, C
and D respectively and leave the tape on f(n + 2).
OUT
IN
MISC.
7542
852
7542
A
7532
852
7532
Continued on next page
INTERPOLATORS
191
19. (continued)
OUT
IN
MISC.
852
B
7
852
B
7532
852
C
7532
D
7
20. Assuming the tape is on interpolator I and standing on
f(n - 2) read f(n), f(n + 1) and f(n + 2) to ctrs. A, B and
C respectively and leave the tape on f(n).
753
85
753
85
A
753
85
B
753
C
754
754
(24) The coefficients may be read from a functional tape using these codes .
21. Position the tape on interpolator II to the argument next
lower than x in ctr. A and read the three interpolational
coefficients to ctrs. B, C and D.
OUT
IN
MISC.
A
76541
641
762
Other computations in-
serted here must cover
tape positioning time .
73
851
7531
851
B
7531
851
C
7531
D
7
(25) Several values at known intervals may be read out in zero order interpolation. The tape is
punched x Jf f(x 1 ), x 2 , f(x 2 ), ... .
22 . If the tape is on interpolator HI, and x n ^x<x n+ j,x
lies in ctr. A, read f(x n _ j), f(x n ), f^ + j\ to ctrs. C, D
and E respectively. Insert sufficient operations to cover
tape positioning time . Leave the tape standing on an
argument.
OUT
IN
MISC.
A
76542
641
762
Continued on next page
192
CODING
22 . (continued)
OUT
IN 1 MISC.
Other computations in-
serted here must cover
tape positioning time .
73
852
7542
C
7532
852
7532
D
7532
852
7532
1
1
i._
! E
7532 |
(26) The interpolators may be used to evaluate any function of the form
f(x) = C Q + C lg (x) + C 2 (g(x) ) 2 + C 3 (g(x) ) ...
where g(x^ is anv function of x computed in the machine. The functional tape is punched as
usual with the argument and the coefficients C k , C k . V ..., C Q , in that order Plugging must
be checked for the complete read-in to the intermediate counter. This saves the build-up time
in * a rh multiplication of the computation of the series. If the C k are functions of x, then x
would usualtyhave to be an integral multiple of the tape interval, ax. If the C k are constants,
the argument line is not punched except for the argument code.
x lies in ctr. A. g(x) lies in ctr. B. The tape is on
interpolator I. Evaluate f(x) as defined above and
deliver f(x) to ctr. C. Omit (A) in the first line if the
C k are constants.
OUT
TXT
(A)
7654
62
B
763
C
73
1
7
1 '
(27)
If it is not desirable to cover tape -positioning time and if it is necessary to initiate operations
other than the usual interpolation sequence as soon as the proper argument is located, the tape
selection relays may be dropped out by the two lines of coding (blank, blank, 761; blank, blank,
762) immediately following the first two normal lines of coding.
24. From the value tape on interpolator I read out two functions
associated with the argument x , which lies in ctr. A. Store
the functions in ctrs. B and C. Leave the tape on an argu-
ment.
OUT
IN
MISC.
A
7654
62
Continued on next page
INTERPOLATORS
193
24. (continued)
OUT
IN
MISC.
761
762
73
85
753
85
B
753
C
753
(28) The two dial switches above an interpolator need not be set alike. The right dial switch must
be set to the number of values accompanying an argument in the tape in order to position the
tape. The left dial must be set to the number of these values to be used in the interpolation
computation.
25 . On interpolator I there is a functional tape with seven
coefficients to be used on a problem where five coef-
ficients will give the necessary accuracy . Set the right
dial switch to seven and the left dial switch to five.
After locating the argument, drop out the tape selection
relays, step twice to eliminate Cg and C 5 from the com-
putation, and proceed to interpolate using C 4 to Cq. Ctr.
A contains x. Deliver f(x) to ctr. B.
OUT
IN
MISC.
A
7654
62
761
762
753
753
841
7654
A
763
B
73
7
(29) Special problems may require unusual applications of the interpolators. For example, "h"
correction-2 or "h" correction-3 may be stored in counter C by the line of coding (841, C,
blank) in conjunction with special wiring. See Plugging Instructions. The interpolator sequence
can be used for shifting or clipping numbers by plugging the intermediate counter for the proper
shift and using a tape punched with three repeated lines reading (a) argument code only, (b)
unity, (c) blank. In this case no Out code is used on the first line and on the third line the Out
code is for the counter containing the number to be shifted.
Multiple Use of Interpolators
(30) When two or three functions have the same range of the independent variable and can be repre-
sented to the desired accuracy with the same interval of the argument and the same number of
interpolational coefficients punched with the same decimal point, the functional tapes will be
194
CODING
identical except for the numerical values of the coefficients. Under these circumstances , it
mov \y e desirable to "osition two or three tapes simultaneously. Only one tape positioning is
coded in the main sequence tape and the "Interpolator gang-positioning switches" control the
positioning of the one or two remaining tapes.
(31) This coding involves the operational code 61 in the Miscellaneous column. Therefore the read-
in of the argument may not be subject to an operational code and sufficient cycles must be in-
serted to cover maximum tape positioning time.
(32) Other calculations may be performed between the computations of the several interpolations or
not as desired.
(33) It should be noted that the number of interpolational coefficients may be made identical by in-
cluding zero coefficients. See Design of Functional Tapes. (Such zero coefficients consume
only four cycles of machine time.)
26. x lies in sw. or ctr. A. Read f(x), g(x) and h(x) from
interpolators I. n and HI to ctrs. B, C,and D respectively.
Use interpolator I as a control for positioning the three
tapes simultaneously.
/-VTITP
TXT
J.A-1
MISC.
A
7654
61
762
Other computations in-
serted here must cover
tape positioning time.
841
7654
A
763
B
7
7
Other computations of
any length, if desired.
841
76541
A
763
i
C
7
r?
Other computations of
any length, if desired.
841
76542
A
763
D
73
■
7
— .
195
DESIGN OF FUNCTIONAL TAPES
(1) The interpolators are designed for all orders of interpolation up to and including the eleventh
order.
(2) Interpolation is carried out by means of the interpolation^ polynomial:
f(a + h) * C + C h + C_h 2 + ...
U J. £*
where
x = a + h, the amount standing in a given storage counter for which f(x) is to be com-
puted,
a = the argument in the tape which most closely approximates x and for example:
C Q = f(a), ..., C k = f^ayk! •
(3) Numbers are punched in a functional tape in accordance with a four row code discussed in the
physical description of the machine .
(4) Negative arguments and coefficients are punched as complements on nine. It is desirable that
tapes be designed with the decimal point between columns 15 and 16 unless the accuracy desired
requires more decimal places.
(5) The punched arguments are distinguished from all other values by the argument code punched
in the lowest order machine column.
(6) The values of the argument, a, must be punched in columns 15, 16, 17, 18 and 24 (for the alge-
braic sign), the lowest order column of the argument being punched in the fifteenth column. The
maximum range of the argument must be encompassed in four powers of ten. The interval of
the argument must be a power of ten, positive or negative; i.e., a a = 10 11 . Hence the maximum
value of h is 0.5 x 10 11 . A tape must include an even number of arguments. When using a func-
tional tape, one half the number of arguments, N/2, must be set up in the push button switches
labeled "Value tape set up 1/2 "A" values in tape" above the interpolator.
(7) For each value of the argument the values punched in the tape in order are:
the argument and the argument code in the first column,
the coefficient C,,
the coefficient C fc « ,
the coefficient C« ,
the coefficient Cq.
The number of interpolational coefficients (including C fl ), k+ 1, is set in the dial switches
labeled "Set up number of "C" values on each switch".
(8) The interpolators require plugging to care for the argument, the decimal point, the "h" cor-
rection and the "C" values. If the tape contains negative "C" values, tire decimal point may not
be shifted to the right. The highest order "h"; i.e., the number of the column containing 10n-l,
must be specified for the proper plugging of functional tapes.
196
CODING
(S) The maximum tape positioning time \vnv half the length uf the tape; for intci pGiauOn o* or«er
k is
P = 8 + N(k + 2)/2 cycles,
where
N = number of arguments punched in tape,
k + 1 = number of interpolational coefficients including Cq.
(10) The computation time for interpolation of order k is
C = 7 + k(4 + n 1 ) cycles,
where
k + 1 = number of interpolational coefficients including Cq,
n 1 = n if the maximum number of digits in any interpolational coefficient is even, 2n,
or n 1 = n + 1 if the maximum number of digits in any interpolational coefficient is odd, 2n + 1 .
(11) The design of a functional tape for interpolation of order k involves the specification of:
1. the accuracy of the tape,
2. the range of the argument and any special coding devices by which the range may be in-
creased,
3. the interval of the argument,
4. the number of arguments, N.
5. the number of interpolational coefficients, k + 1 f
6. the tape decimal point .
(12) For any specific range of the argument and any predetermined accuracy, a function may be
represented by a functional tape in several different ways. Many interpolational coefficients
may be used with large intervals of the argument, giving a short tape, brief positioning time,
but long computation time. On the other hand, a small interval of the argument with few interpo-
lational coefficients will result in short computation time but longer positioning time. In general,
a +ape should be so designed that the sum of the mean positioning time and the computation time
will be a minimum. If, however, it is known that the successive arguments for which interpo-
lation is to be performed differ but little from one another, the positioning time is small in any
case, and it will be more effective to design the tape for minimum computation time. If the
variable is random and expected to vary by large increments, it is desirable to design the tape
so that positioning time is a minimum and spend a longer time on computation. Thus the design
of a functional tape is governed in the main by three factors: accuracy, tape positioning time
and computation time.
(13) In computing the accuracy of a tape, if k is the index of the last interpolational coefficient, k is
determined by
oo
r = , II C. (h max) 1
k+ 1 l
where the remainder, r, must be less than one half unit in the lowest order column required to
give the desired accuracy. When Taylor's series is used, k is determined by
k 4. 1
r :£ Cy. M 1 (h max)
taking for CV « its maximum value as a function nf x in the ranee under rrmsiHoT-atlrm
K + i. ............ ._ - — .... „_ -..w...
197
DESIGN OF FUNCTIONAL TAPES
1. As an example of the design of a functional tape consider f(x) = arc tan x (principal values).
By a coding device employing the identities
arc tan (-x) = - arc tan x
and
arctan|x| = nr/2 - arc tan l/|x|,
a tape covering the arguments s x <; 1 may be extended to cover interpolation for
-oosxs+oo. Using Taylor's series, the coefficients of the interpolational polynomial
C = f(a) = arc tan a
C = f(a) =
1 + a 2
c,=i^U -a
2 2- (1 + a 2 ) 2
r - f "'( a ) 3a 2 - 1
\,n _ — — — s — — — — — —
3'. 3(1 + a 2 ) 3
3
C * 1V (a) a - a
4 41 (1 + a 2) 4
C = f v (a) ^ 1 - 10a 2 + 5a 4
5 5». 5(1 + a 2 ) 5
The absolute value of all coefficients is less than or equal to one.
The following table shows the calculations for accuracy, tape positioning time in cycles
and computation time in cycles. The accuracy desired is an error of not more than 5x 10-8
and the tape is punched with decimal point between columns 9 and 10.
Calculations for Tape for f(x) = arc tan x
Tape number
I
n
ni
Interval of argument
0.1
0.01
0.001
Range of arguments
0<xs£l.l
0^x^1.01
0<x< 1.001
Number of arguments = N
12
102
1002
C. (h max)
5 x 10" 2
5 x 10" 3
5 x 10" 4
C 2 (h max) 2
—
8.125 x 10* 4
8.125 x 10" 6
8.125 xl0~ 8
198
CODING
/-i_i_..i_4.j — „ *,>■». T>o»-i£i fnv f(v\ — arf> ts»n -v ^continued)
Tape number
Co (h max)*
C 4 (h max)'
C_ (h max)
5
Number of coefficients = k + 1
Tape positioning time in cycles...
Maximum
Mean
Computation time in cycles
Interpolation time in cycles..
Maximum
Mean
Error of tape
4.2x10
-5
2.5 x 10
6.3 x 10
29
52
102
81
n
4.2x10"
2.5 x 10
10
6.3 x 10
-13
4x 10
110
ZD
237
135
4.3 x 10
m
4.2 x 10
-11
2.5 x 10
-14
6.3 x 10
•18
9ni5!
1010
2037
1035
4.3 x 10
■11
(14) Since the number of coefficients required for the desired accuracy varies with the argument,
u *' 7T. „ Jl w * k„ ™ — w„«. «r nc in ninrA of the hierher coefficients for values
computation unit* ui<*y uc oovcu uj |/u«vuu. b ~~- — --- 1 ~ .,, j. j. j •
of the argument not requiring as many terms of the series. Since the MC is held constant during
the computation, a multiplication by zero consumes only four cycles in such cases.
2. For example, consider f(x) = arc sin x. The tape is to be punched for 0< x < 0.9, the in-
tervals of the argument being 0.01.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Calculations for Tape for f (x) = arc sin x
C . (h maxp
- 4 v /
2.45 x 10" JJ
5.56 x 10" 11
1.04xl0-J0
1.91x10-1°
3.74 x 10" 10
8.31 x 10" 10
2.30 xlO -9
9.56 x 10" s
1.09 x 10" 7
C- (h max) 5
o :
o oc ~ 1 rt-13
2.65 x 10-JJ
3.73 x 10" 13
6.24 x 10" JJ
1.21x10" J 2
2.71 xlO" 12
7.38 x 10- 12
2.70 x 10" l \
1.68x10-1°
3.81 x 10' 9
C c (hmax) 6
5.30x10" J*!
1.36 xlO" 15
3.07 xlO" 15
7.34 x 10" 15
2.02 x 10" 14
6.97 x 10" 14
3.37 xlO" 13
3.12 x 10" 12
1.32X10" 10
C„ (h max) '
6.20 x 10" J 5
5.62 x 10" 11
199
DESIGN OF FUNCTIONAL TAPES
Thus a tape with an error of e < 6 x 10" 11 due to the termination of the Taylor's series
would be punched with the following coefficients:
sa<0J
0.2<a<0.7
0.7<a<0.8
0.8<a<0.9
a, 0, 0, 0, C 3 , C 2 , C p C Q
a, 0, 0, C^, Cg, C2> Cj, Cq
a > **> Cg, C^, Cg, C2J Cp Cq
a, Cg , C g , C 4 , Cg, C 2 , Cj, C Q
Thus for random values of x, Tape I is the most effective. If, however, it were known that
the values of x were increasing and that in no case was ax 5r 0.1, the positioning time of
Tapell would be reduced to 48 cycles or less, giving a maximum interpolation time of only
76 cycles and making Tape II the more efficient. For the desired accuracy, Tape HI is ob-
viously inefficient.
(15) With the possible exception of very elementary functional tapes, the values of the interpolation
coefficients should be computed on the calculator itself. Hence the design of a functional tape
involves the coding of a sequence tape for its preparation.
(16) To facilitate punching of the functional tape, the sequence tape calculating the coefficients should
be so coded that it prints the argument, followed by the coefficients in the order C, , C
'l» c
Negative numbers should be printed as complements on nine.
k' ^k-1 1
(17)
Before the functional tape is used in a calculation, there are two checks which should be made
using the calculator. The interpolator should be required to position on each argument and to
print out the successive coefficients (the argument cannot be printed from the tape because of
the argument code in the first column). This set of coefficients should then be proof-read
against the computed coefficients. The coding for the sequence tape to accomplish this, if the
functional tape has three interpolational coefficients, is given in example 3.
3. Test arguments and read out three coefficients.
Functional tape on interpolator I.
accumulate argument in ctr . 1
position tape
drop out tape selection relays
reset interpolation check counter
print argument on typewriter I
step ahead, read and print C
OUT
IN
MISC.
87
8431
1
7
1
7654
62
761
762
73
1
7432
752
6
85
753
7432
752
6
Continued on next page
200
CODING
3 . (continued)
Step ahead, read and print C^
Step ahead, read and print C Q
OUT '
IN
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85
753
7432
752
6
85
753
7432
752
6
87
The operating instructions for this tape must include plugging instructions for interpolator
t i ±_»— .—1+^.. T r«r. moll «o fVia f r\\ 1 mm ner inctT"iii»tir*TIK:
k ctllU ljf|JCWllici i, a.o nCn a.Q u»v- n/^vn...,, ..»«,
A. Reset counter 1 before starting.
B. Set IVS for first value of the argument.
C. Start machine and press 87 stop key.
D. If interpolator does not position, check tape to see that first argument and argument
code are in proper position. If these are correct, test interpolator.
E. When machine stops on 87, reset IVS to 1 x 10 n where Aa = 10 n . Restart machine.
F. For each argument the interpolator may fail to position. If the interpolator does not
position, check tape to see that the appropriate argument and argument code are in
proper position.
The interpolator should also be required to interpolate on assigned values of x which can
be checked against tables. In general, it is wise to check the mid-values, since these give
rise to approximately the maximum error. The coding for such a tape is given in example 4.
4. Test interpolation. Tape on interpolator I.
reset ctr. 2
accumulate argument in ctr. 1
position and interpolate
OUT
IN
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on
U 1
2
2
7
8431
1
7
1
7654
62
841
1
763
DESIGN OF FUNCTIONAL TAPES
201
4. (continued)
read f(x) to ctr. 2
print x on typewriter I
print f(x) on typewriter I
OUT
IN
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2
73
7
1
7432
752
6
2
7432
752
6
87
The operating instructions for this tape must include plugging instructions for interpolator
I and typewriter I, as well as the following instructions:
A. Reset counter 1 before starting.
B. For the first round of sequence tape set IVS equal to the first value to be checked, then
change to ax. If it is desired to interpolate on mid- values on a tape starting with argu-
ment zero, set IVS = 5 x 10 n " 1 for the first round and IVS = 10 n thereafter, where
Aa = 10 n .
(18) One interpolator can be made to serve for several functions by subjecting the arguments to a
linear transformation and punching them in a single tape. In this case, the interval of the
transformed arguments and the number of interpolational coefficients must be equal for all
functions. The number of interpolational coefficients may of course be made identical by using
zero coefficients which consume only four cycles of machine computation time.
A tape is to be designed for
y = f(x)
0s as x«= b
y = g(x)
0< c< x< d.
The tape must be punched for
F(z)
< a < z *= bd/c
where
F(z) = f (x)
a< z< b
F(z) =
z =b
F(z) = g(cz/b)
b< z< bd/c
For y = f(x), the argument is read directly to the interpolator.
For y = g(x), z = bx/c is read to the interpolator as the argument.
Care must be taken in selecting the limits a, b, c and d of the functions, so that the interpo-
lator is not required to position to the argument z = b .
202
METHODS OF DIFFERENCING
ft \ t_ . n u,.i n fi'n<r fh Q e„/./»occi«D Aiftaranoaa ni a function, thrive schemes for the use of counters
are available. To calculate nth differences^ the first method consumes 3n cycles and uses n
counters. The second or "round-robin" method covers n + 2 cycles, uses n + 1 counters, and
must be repeated n + 1 times. The third method covers 2n + 2 cycles and uses n + 1 counters.
(2) If a computation includes sufficient multiplication and division so that many lines are free for
interposed operations, and if there is a shortage of counters, the first method is appropriate,
(3) If the coding is tight and if the computation is brief so that repetition will not make too long a
tape, the second method is more efficient.
(4) In most other cases except first order differencing, the third method is most useful. Note that
this method provides a simple check on the result.
(5) The first method is coded to compute and print fifth differences.
1. The value u n lies in ctr. P and may therefore be inverted when read out, and
counter A = u_j
counter B = au_2
counter C = a^u_3
counter D = a^u_4
5
counter E = a^u
- u« to ctr. A; A = -au_^
2
- au_j to ctr. B; B = -a u_ 2
- a^ ~ to ctr. C: C = -a 3 u „
-& ■ -o
% 4
- a°u_ 3 to ctr. D; D = -a u_ 4
- a^u_ 4 to ctr. E; E = -a u_ 5
print a u_gon typewriter I
reset ctr. E
4
a n . to ctr. R
_ __ 4
reset ctr. D
3
a u_« to ctr. D
reset ctr. C
a 2 u „ to ctr. C
T-gogt ctr ^
OUT
IN
MISC.
P
A
732
A
B
7
B
C
7
C
D
7
D
E
7
E
7432
32
752
6
E
E
n
i
D
E
732
D
D
7
C
D
732
C
C
7
B
C
732
B
B
7
Continued on next page
METHODS OF DIFFERENCING
203
1 . (continued)
au_j to ctr. B
reset ctr. A
u to ctr. A
OUT
IN
MISC.
A
B
732
A
A
7
P
A
7
2. The value u« lies in a value tape or arises from any sources from which the read-out
cannot be inverted, and
counter A = -u_j
counter B = -au_2
counter C = -a^u.^
counter D = -a**u_4
counter E = -a^u c .
Uq to ctr. A; A = au_,
au_| to ctr. B; B = a2u_«
a2u_« to ctr. C; C = a^u,
a^u_ 3 to ctr. D; D = a 4 u_ 4
a 4 u_ 4 to ctr. E; E = a 5 u_ 5
print a 5 u_ 5 on typewriter I
reset ctr. E
-a 4 u_4 to ctr. E
reset ctr. D
-a^u_3 to ctr. D
reset ctr. C
-a^u_2 to ctr. C
reset ctr. B
-au_^ to ctr. B
reset ctr. A
u to ctr. A
OUT
IN
MISC.
P
A
7
A
B
7
B
C
7
C
D
7
D
E
7
E
7432
752
6
E
E
7
D
E
732
D
D
7
C
D
732
C
C
7
B
C
732
B
B
7
A
B
732
A
A
7
P
A
732
(6) The "round -robin" method is coded to compute and print third differences.
204
CODING
3. Successive values of the function are delivered from
value ta™e card feed or ctr. P and
counter A = - a u_4
counter B = a 2 u_3
counter C = -au_2
counter D = u_j .
reset ctr. A
u to ctr. A
-u Q to ctr. D; D = -au_j
au_j to ctr. C; C = a u_ 2
2 3
- A _ u_ 2 to ctr . B; B = - a u „
print a u_„
reset ctr. B
u« to ctr. B
-Uj to ctr. A; A = -au q
AU Q to ctr. D; D = a^u_ 1
.2
print A a u_ 2
a 2 ^! to ctr. C; C = -a°u_ 2
reset ctr, C
u 2 to ctr.C
-u 2 to ctr.B; B = -au x
au, to ctr. A; A = a 2 u q
-a 2 u to ctr. D; D = -a 3 u_ 1
print a 3 u_ 1
reset ctr. D
u 3 to ctr. D
OUT
B
B
B
IN
D
B
7432
752
MISC.
732
732
32
732
732
I nto
u
\s
■ wu
c
7432
32
752
6
c
C
7
p
C
7
Ir
1
in
1732
~ 1
~ 1
B
A
732
A
D
732
D
7432
32
752
6
D
D
7
[P
1
P
7
Continued on next page
205
METHODS OF DIFFERENCING
3. (continued)
-u 3 to ctr.C; C = -au 2
AUoto ctr. B; B = Ani^
-auj to ctr. A; A = - a uq
print a u
OUT
IN
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D
C
732
C
B
732
B
A
732
A
7432
32
752
6
(7) The third method is coded to compute and print fifth differences.
4. Successive values of the function are delivered from a value tape, card feed or ctr. P and
counter A = u_i
counter B = au 2
counter C = AV3
counter D = a 3 u_4
counter E = a 4 u_5
counter F = A^u_g .
reset ctr. F
-a^u_5 to ctr. F
-a^u_4 to ctr. F
-a^u_3 to ctr. F
-au_ 2 to ctr. F
-u_jtoctr.F
u to ctr. F; F = a 5 u_ 5
print a 5 u_5 on typewriter I
a 5 u_ 5 to ctr. E; E = a 4 u_4
a 4 u_4 to ctr. D; D - a 3 u_3
A 3 u_ 3 to ctr. C; C = a 2 u_ 2
a2u_2 to ctr. B; B = au_i
au_i to ctr. A; A = uq
Note that an excellent check on the accuracy of the differencing process can be made in
three additional cycles by checking u Q in A against P.
OUT
IN
MISC.
F
F
7
E
F
732
D
F
732
C
F
732
B
F
732
A
F
732
P
F
7
F
7432
752
6
F
E
7
E
D
7
D
C
7
C
B
7
B
A
7
206
CENTRAL-DIFFERENCE INTERPOLATION
(1) "A central-difference formula terminating at a mean difference of the entry u« is more accu-
rate man a tormina wmcn is curtailed at the corresponding difference oi u < m , and it is
less accurate than a formula which is curtailed at the corresponding difference of u i /o • "
Whittaker and Robinson, The Calculus of Observations , 3rd ed„ London, 1940, p. 49.
Thus the Newton-Bessel formula is more accurate as far as mean differences of even order
when further terms are neglected than the corresponding Newton-Stirling formula. In the same
way Newton-Stirling is more accurate as far as mean differences of odd order .
If interpolation is being performed on third differences, the Newton-Stirling formula is the more
accurate since it terminates in mean third differences. Since operations are inserted during
tape positioning time and interposed during multiplication, the cost of including the term con-
taining the fourth difference is but one multiplication. Because of this gain in accuracy, the
formula has been coded to include the fourth difference term. The computations of the coef-
ficient, fourth difference and the completed term have been underlined so that they may easily
be omitted if desired. For even differences the same considerations apply to the use of the
Newton-Bessel formula.
:ss:irr.cH in this: saftinn that 2 iahle rvf
irtinn
srsH fhi
has
been punched with an argument of the form a + kw, followed by the value of the function f(a + kw),
for k = 0, 1, ..., 9, and all values of a required. The integer n and the parameters a and w
are fixed, for a particular case, and are connected by the relations w = 10~ n , n = 0, a a = lOw.
It is now desired to compute f (y) by interpolation, where y is within the range of the arguments
on the tape. The coding first puts the argument y in the form a + xw, where x is now not
necessarily an integer, and where < x < 10,
(3) The value y is sent to the interpolator to position the tape to the tape argument, a, immediate-
ly below it; i s e i} such that = y - a < lOw* The tape positioning time^ which must be covered,
since the tape is being positioned to the next lower value of the argument, is used to determine
x and the coefficients involving x. If the tape positioning time cannot be covered, the usual
coding is used and the first column of the interpolation counter is not plugged. See Plugging
Instructions .
(4) The method of computation of x during tape positioning time, when a is still unknown and w is
a power of ten, is shown below.
(a)
If w = 10~ n , n a positive integer or zero, then a + xw is shifted n columns to the left by
passing it through the LIO counter. The LIO counter is plugged for such a shift except that
the plugging is omitted in the columns above one to the left of the decimal point and nines
are plugged into the first n machine columns of the buss. This will finally give x if y is
positive, and x - 10"P if y is negative, where the position of the decimal point is between
columns p and p + I . A correction is made by adding five in column 24 and then subtract-
ing five in column 24 under control of the choice counter. Thus x is the result in either
case.
1. a + xw lies in ctr. A; sw. P contains 5 in col. 24. Deliver x to ctr. B.
reset LIO ctr.
a + xw to LIO ctr.
reset ctr. B
OUT
IN
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A
765421
7
B
B
7
\^l/Xll..LJ..IUl'L r U \Jik
CENTRAL-DIFFERENCE INTERPOLATION
207
OUT
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831
B
7
732
732
7
A
732
732
P
B
7
P
B
7432
1 . (continued)
x to ctr. B
reset ctr. 70
- (a + xw) to ctr. 70
5 in 24th column to ctr. B
5 in 24th column to ctr. B under control of ctr. 70
(b) If w = 10 n , n a positive integer, it is in most cases better to normalize the units of the
argument and of the function to include this in the previous case.
(5) In the coding which follows it is assumed that a a = 0.1 in the tape, and that the tape is on
interpolator I. It is also assumed that the successive values of a + xw appearing in the compu-
tation do not differ by more than one unit. If they differ by more than one unit more cycles
must be added to cover tape positioning time. If it is known that the values of a + xw occur in
close succession, it might be profitable to defer at least a part of the computation of the coef-
ficients until the tape has positioned, and use these multiplications to cover the differencing.
This is particularly true of computations involving the higher order differences.
(6) For interpolation extending through third or fifth differences, the Newton-Bessel formula was
used:
f(a + xw) = 1/2 [f(a) + f(a + w)] + (x - 1/2) A f (a) + x( ^J " 1/2 [ A 2 f(a - w) + A 2 f(a)]
+ x(x- l)(x-l/2) A 3 f(a . w) + (x + Wx-lKx-2) 1/2 [A4f(a _ ^ + ^ _ ^
+ (x+Dx(x-l)(x-2)(x-l/2) A s f(a _ 2w)
51
2. a + xw lies in ctr. A. f(a + xw) is to be delivered to ctr. L. Ctrs. B through L, 70 and LIO
are available for computation, but not reset. Switches are set as follows:
Switch SP = 1/2
Switch SQ =1.0
Switch SR = 1/4
Switch SS = 2/3
Switch ST = 5 in machine column 24 .
Coefficients for and computation of third differences which may be omitted are underlined.
(7) s must be omitted if no operations are interposed.
(a + xw) to interpolator I
interpolator I positions
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641
762
Continued on next page
208
CODING
2 . (continued)
reset LIO ctr.
(a + xw)to LIO ctr.
reset ctr. B
xtoctr.B
reset ctr. 70
- (a + xw) to ctr. 70
5 in column 24 to ctr. B
7 5 in column 24 to ctr. B under control of ctr. 70
ygoQt ctr. M
x to ctr. M
x toMC
- 1 to ctr. B
reset ctr. C
(x - 1) to MP
1/2 to ctr. P
reset ctr. D
reset ctr. E
reset ctr. F
x(x - l)to ctr.C
x(x - 1) to MC
reset ctr. N
reset ctr. G
1/4 to MP
reset ctr. H
reset ctr. I
reset ctr. J
OUT
IN
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763
A
765421
7
B
B
7
831
B
7
732
732
7
A
732
732
ST
B
7
ST
B
7432
M
M
7
B
M
7
B
761
7
SQ
B
732
C
C
M
7
SP
P
7
D
D
7
1
E
E
7
F
F
7
C
761
7
V
N
1
N
7
G
G
SR
7
H
H
7
I
I
7
J
J
7
Continued on next page
CENTRAL-DIFFERENCE INTERPOLATION
209
2 . (continued)
reset ctr. K
x(x - l)/4 to ctr. N
x(x - l)/4 to MC
- 1/2 to ctr. P
x to ctr. P
(x - 1/2) to MP
x(x - l)(x - 1/2) /4 to ctr. D
x(x - l)(x - l/2)/4 to MC
reset ctr. L
reset ctr. Q
2/3 to MP
OUT
IN
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K
K
N
7
N
761
7
SP
P
732
B
P
P
(7)
D
7
D
761
7
L
L
7
Q
Q
s.
m
Q
'-
x(x - l)(x - l/2)/3l to ctr. Q
A check should be made to see that sufficient cycles have been inserted to cover interpo-
lation positioning time.
interpolator I has positioned; reset IC
select interpolator I and step ahead
f(a) to ctr. E and step ahead
select interpolator I and step ahead
f(a + xw) to ctr. F and step back
Continued on next page
73
85
753
E
753
85
753
F
754
210
CODING
2 . (continued)
1/2 to MC, step back
f(a) to etr. K, step back
f(a + w) to ctr. K, step back
[f (a) + f (a + w)] to MP
f(a + w) to ctr, G.
-f(a)to ctr.G; G = Af(a)
select interpolator I
f(a - w) to ctr. H, step ahead
Iffa^ + f(a + w^ I /2 tn r.tr L-. st^n ahead
(x - 1/2) to MC, step ahead
- f(a) to ctr. H; H = -Af(a - w)
Af(a) to ctr. H; H = A 2 f(a - w), step ahead
Af(a) to MP, step ahead
select interpolator I, step ahead
f(a + 2w) to ctr. I
- f(a + w) to ctr. I; I = Af(a + w)
- Af(a) to ctr. I; I = A 2 f(a)
(x- l/2)Af(a)toctr.L
x(x - l)/4 to MC
2
a f(a - w) to ctr. J
2
a f (a) to ctr. J
[a 2 f (a - w) + A 2 f(a)] to MP
- A 2 f(a - w) to ctr. I; I = A 3 f(a - w)
/-virnn
TXT
ill
MISC.
SP
761
754
E
K
754
F
K
54
K
7
F
G
7
E
G
732
85
7
H
53
L
753
P
761
753
E
H
732
G
H
53
G
753
85
753
ll
i
i
7
F
I
732
G
I
32
L
7
N
761
7
H
J
7
I
J
J
7
H
I
(7)32
I
Continued on next page
211
CENTRAL-DIFFERENCE INTERPOLATION
2. (continued)
x(x - 1) [a 2 £ (a - w) + A 2 f(a)] /4 to ctr. L
x(x - l)(x - l/2)/3l to MC
A 3 f (a - w) to MP
x(x - l)(x - l/2)A 3 f(a - w)/3l to ctr. L.
f(a + xw) lies in ctr. L.
OUT
IN
MISC.
L
7
Q
761
(7)
I
(7}
L
7
(7) For interpolation extending through fourth differences, the Newton-Stirling formula was used:
f(a + xw) = f(a) + x [Af(a) + Af(a - w)] /2 + x 2 /2'.A 2 f(a - w)
+ x(x 2 - l 2 )/3'. [A 3 f(a - w) + A 3 f(a - 2w)] /2 + x 2 (x 2 - l 2 )/4'.A 4 f(a - 2w) + ...
3. a + xw lies in ctr. A. f(a + xw) is to be delivered to ctr. L. Ctrs. B through N, 70 and
LIO are available for computation but not reset. Switches are set as follows:
Switch SP = 1/2
Switch SQ = 5 in machine column 24
Switch SR = 1 .0
Switch SS =1/6
Switch ST = 1/12 .
Coefficients for and computation of fourth differences which may be omitted are under-
lined. (7)'s must be omitted if no operations are interposed.
(a + xw) to interpolator I
interpolator I postion
reset LIO ctr.
(a + xw) to LIO ctr.
OUT
IN
MISC.
A
7654
641
762
763
A
765421
7
Continued on next page
212
CODING
3. (continued)
reset ctr. B
x to ctr. B
reset ctr. 70
- (a + xw) to ctr. 70
5 in first column to ctr. B
+ 5 in first column to ctr. B under control of ctr. 70
x toMC
reset ctr. C
reset ctr. L/
x to MP
- 1 to ctr. D
reset ctr. E
reset ctr. F
reset ctr. G
x 2 to ctr. C
x toMC
x 2 to ctr. D; D = x - 1
reset ctr . H
1/2 to MP
reset ctr . I
reset ctr^ J
reset ctr. K
reset ctr. P
x/2 to ctr. P
x 2 to MC
reset ctr, L
1
OUT '
IN
MISC. !
B ]
B
7
B31 ]
B
7
732
732
7
A
732
732
SQ
B
7
SQ
B
7432
B
761
7
C
C
7
D
D
B
7
SR
D
732
E
E
7
F
F
7
G
G
C
7
B
761
7
C
D
7
H
H
SP
7
I
I
7
I
J
J
7
K
K
7
P
P
P
7
C
761
7
L
i
L
7
Continued on next page
CENTRAL-DIFFERENCE INTERPOLATION
213
3 . (continued)
reset ctr. M
1/2 to MP
reset ctr. N
reset ctr. Q
x 2 /2! to ctr. Q
(x 2 - 1) to MC
x/2 to MP
x(x^ - l)/2 to ctr. E
x(x 2 - l)/2 to MC
1/6 to MP
reset ctr. U
x(x 2 - l)/(2)(3i)toctr.U
x 2 ^ to MC
OUT
IN
MISC.
M
M
SP
7
N
N
(7)
Q
Q
Q
7
D
761
(7)
P
(7)
E
7
E
761
(7)
SS
7
U
U
U
7
9.
761
(7)
Continued on next page
214
CODING
a . (continued )
(x* - DtoMP
reset ctr. R
x 2 (x 2 - l)/2 to ctr, R
x 2 (x 2 - D/2 to MC
1/12 to MP
OUT
IN
MISC.
D
7
fi-
R
R
7
ll
761
(11
ST
1
S_
S
S
7_
reset ctr. S
x 2 (x 2 - D/4 1 . to ctr. S
A check should be made to see that sufficient cycles have been inserted to cover interpo-
lation positioning time.
interpolator I has positioned, reset IC
select interpolator I and step ahead
f(a) to ctr. F, step ahead
select interpolator I and step ahead
f(a + w) to ctr. G, step back
f(a + w) to ctr. H, step back
- f(a) to ctr. H; H = Af(a)
f(a) to ctr. L, step back
select interpolator I and step back
73
85
753
■c
J.-
1 uu
85
753
G
754
G
H
754
F
H
732
F
L
754
85
754
CENTRAL-DIFFERENCE INTERPOLATION
215
3. (continued)
f(a - w) to ctr. I, step back
- f(a - w) to ctr. F; F = Af(a - w)
x/2 to MC, step back
Af(a) to ctr. M
Af(a - w) to ctr. M
Af(a) + Af (a - w) to MP
select interpolator I
f(a - 2w) to ctr. J, step ahead
- f(a - 2w) to ctr. I; I = Af(a - 2w)
- Af(a - w) to ctr. I; I = - A 2 f(a - 2w)
x/2 |_Af(a) + Af(a - w)] to ctr. L, step ahead
x 2 /2! to MC, step ahead
- Af(a) to ctr. F; F = - A 2 f(a - w)
A 2 f(a - w) to ctr. K
A 2 f (a - w) to MP
- A 2 f(a - 2w) to ctr. K; K = A 3 f(a - 2w), step ahead
step ahead
step ahead
reset ctr. T, step ahead
(x 2 /2i)A 2 f(a -w) to ctr. L, step ahead
select interpolator I
f(a + 2w) to ctr. T
- f(a + w) to ctr. T; T = Af(a + w)
- Af(a)to ctr.T; T =A 2 f(a)
- A 2 f(a - w) to ctr. T; T = A 3 f(a - w)
x(x 2 - 1)/12 to MC
A 3 f(a - 2w) to ctr. N
OUT
IN
MISC.
I
754
I
F
732
P
761
754
H
M
7
F
M
M
7
85
7
J
753
J
I
732
F
I
32
L
753
Q
761
753
H
F
732
F
K
32
F
732
I
K
753
753
753
T
T
53
L
753
85
7
T
G
T
732
H
T
732
F
T
7
E
761
7
K
N
7
Continued on next page
216
CODING
<? /r»/\r>+TTiiioH\
A 3 f(a - w) to ctr. N
[A 3 f(a - 2w) + A 3 f (a - w)] to MP
- A 3 f(a - 2w) to ctr. T; T = A 4 f(a - 2w)
x(x 2 - l)/3! [A 3 f(a - 2w) + A 3 f(a - w)] /2 to ctr. L
x 2 (x 2 - l)/4!toMC
A 4 f(a - 2w) to MP
x 2 (x 2 - l)/4i A 4 f(a - 2w) to ctr. L.
f(a + xw) lies in ctr. L.
OUT
IN i
MISC.
[
T
N
I
N
7
K
T_
(7)32
L
7
S
761
(I)
T_
(Jl
L_
1
217
INTERPOLATION BY NEWTON- GREGORY DIFFERENCE FORMULA
(1) In certain cases the Newton-Gregory formula of interpolation is found convenient. It may be
used in the form
f(a + xw) =f(a) + x Af(a) + x < x ~ *> A 2 f(a) + x(x - l)(x - 2) A 3 f(a)
+ x(x - l)(x - 2)(x - 3) A 4 f(a) + x(x-l)(x'-2)(x-3)(x-4) A 5 f(a) ...
(2) It is assumed that a functional tape has been punched with the values
..., (a - 2w), f(a - 2w), (a - w), f(a - w), a,
f(a), (a + w), f(a + w), (a + 2w), f(a + 2w), ...
(3) In the coding which follows, it is assumed that the interval of the arguments is 0.1 and that the
tape is on interpolator I. See Central -Difference Interpolation, note (5).
1. (a + xw) lies in ctr. A. f(a + xw) is to be delivered to ctr. I. Ctrs. B through P, 70 and
LIO are available for computation but not reset. Switches are set as follows:
Switch SP = 5 in machine column 24
Switch SQ = 1/2
Switch SR = 1/3
Switch SS =1/4
Switch ST = 1/5
Switch SU = 1/6
Switch SV = 1.0
The computation is carried to sixth differences.
(a + xw) to interpolator I
interpolator I positions
reset LIO ctr.
(a + xw) to LIO ctr.
reset ctr. B
x to ctr. B
reset ctr. 70
- (a + xw) to ctr. 70
5 in first col. to ctr. B
+ 5 in first col. to ctr. B under control of ctr. 70
reset ctr. C
OUT
IN
MISC.
A
7654
641
762
763
A
765421
7
B
B
7
831
B
7
732
732
7
A
732
732
SP
B
7
SP
B
7432
C
C
7
Continued on next page
218
CODING
1 . (continued)
x to MC
x to ctr. C
- 1 to ctr,C; C =x - 1
x - 1 to MP
reset ctr. D
reset ctr. E
reset ctr. F
x(x - 1) to ctr. D
ctr. D to MC
reset ctr. Q
- 1 to ctr. C; C =x - 2
1/2 to MP
reset ctr . G
reset ctr. H
reset ctr. I
x(x - l)/2 to ctr. Q
ctr. QtoMC
reset ctr. J
reset ctr ""
(x - 2) to MP
reset ctr. L
reset ctr. M
reset ctr. N
x(x - l)(x - 2)/2! to ctr. E
ctr. E to MC
reset ctr. R
OUT
! TM
MISC.
B
761
7
B
C
7
SV
C
32
C
7
D
D
7
E
E
7
F
F
D | 7
D
761
i
Q
Q
7
SV
C
32
SQ
7
G
G
7
! K
H
1
7
I
1
I
! 1
1 l«
7
Q
761
7
J
J
7
K
K
C
7
L
L
7
M
M
7
N
N
E
17
1
E
761
7
R
R
7
Continued on next page
219
INTERPOLATION BY NEWTON-GREGORY DIFFERENCE FORMULA
1 . (continued)
- 1 to ctr. C; C =x - 3
1/3 to MP
reset ctr. O
reset ctr. P
x(x - l)(x - 2)/3!
ctr.RtoMC
x - 3 to MP
x(x - l)(x - 2)(x - 3)/3! to F
ctr. F to MC
reset ctr. S
- 1 to ctr. C; C =x - 4
1/4 to MP
x(x - l)(x - 2)(x - 3)/4! to ctr. S
ctr. S to MC
x - 4 to MP
OUT
IN
MISC.
SV
C
32
SR
7
7
P
P
(7)
R
7
R
761
(7)
C
(7)
F
7
F
761
7
S
S
7
SV
C
32
ss
(7)
s
7
s
761
(7)
c
(7)
Continued on next page
220
CODING
f/»nnHmi«rf\
x(x - l)(x - 2)(x - 3)(x - 4)/4! to ctr. G
ctr. GtoMC
reset ctr. T
- 1 to ctr. C; C =x - 5
1/5 to MC
x(x - l)(x - 2)(x - 3)(x - 4)/5! to ctr. T
ctr. T to MC
reset ctr. V
x(x - l)(x - 2)(x - 3)(x - 4)(x - 5)/5! to ctr. H
ctr. H to MC
reset ctr. U
1/6 to MP
1 Attm
UU1
i _
in
1 „~ 1
MIov_.
G
7
G
761
7
T
T
7
SV
C
32
ST
(7)
T
7
T
761
(7)
v
V
C
(7)
i
H
7
H
761
7
U
U
(7)
SU
(7)
i
Continued on next page
INTERPOLATION BY NEWTON-GREGORY DIFFERENCE FORMULA
221
1 . (continued)
x(x - l)(x - 2)(x - 3)(x - 4)(x - 5)/6! to ctr. U
reset IC
select interpolator I and step ahead
f (a) to J, step ahead
f (a) to V
select interpolator I and step ahead
f(a + w) to K, step ahead
x to MC, step ahead
f (a) to I
- f (a + w) to J; J = - Af (a)
Af(a) to MP
select interpolator I
f(a + 2w) to L, step ahead
- f(a + 2w) to K; K = - Af (a + w)
Af(a + w) to J; J =A 2 f(a)
x Af(a) to I, select interpolator I and step ahead
f(a + 3w) to M, step ahead
x(x - l)/2! to MC, step ahead
- f (a + 3w) to L; L = - Af(a + 2w)
Af (a + 2w) to K; K = A 2 f (a + w)
A 2 f (a) to MP
- A 2 f (a + w) to J; J = - A 3 f (a)
select interpolator I
f (a + 4w) to N, step ahead
- f(a + 4w) to M; M = - Af(a + 3w)
OUT
IN
MISC.
U
7
73
85
753
J
753
J
V
7
85
753
K
753
B
761
753
J
I
7
K
J
32
J
732
85
7
L
753
L
K
732
K
J
32
85
I
753
M
753
Q
761
753
M
L
732
L
K
32
J
7
K
J
732
85
7
N
753
N
M
32
Continued on next page
222
CODING
i ^continued ^
x(x - l)/2! A 2 f(a) to I, step ahead
x(x - l)(x -2)/3! to MC
Af (a + 3w) to L; L = A 2 f (a + 2w)
- A 2 f (a + 2w) to K; K = - A 3 f (a + w)
A 3 f(a) to MP
A 3 f (a + w) to J; J = A 4 f(a)
select interpolator I
f (a + 5w) to O, step ahead
- f(a + 5w) to N; N = - Af (a + 4w)
x(x - l)(x - 2)/3! A 3 f(a) to I, step ahead
x(x - l)(x - 2)(x - 3)/4! to MC
Af (a + 4w) to M; M = A 2 f (a + 3w)
- A 3 f(a + 3w) to L; L = - A 3 f (a + 2w)
A 4 f(a) to MP
A 3 f (a + 2w) to K; K = A 4 f (a + w)
- A 4 f(a + w) to J; J = - A 5 f (a)
select interpolator I
f(a + 6w) to P
x(x - I)(x - 2)(x - 3)/4! A 4 f(a) to I
x(x - l)(x - 2)(x - 3)(x - 4)/5! to MC
- f (a + 6w) to O; O = - Af (a + 5w)
Af(a + 5w) to N; N - A 2 f (a + 4w) .
A 5 f(a) to MP
- A 2 f(a + 4w) to M; M = - A 3 f(a + 3w)
A 3 f (a + 3w) to L; L = A 4 f (a + 2w)
- A 4 f (a + 2w) to K; K = - A 5 f (a + w)
OUT
IN
MISC .
I
753
R
761
7
M
L
732
L
K
32
J
732
K
J
732
85
7
O
753
Q
N
32
I
753
s
761
7
N
M
732
M
L
32
J
7
L
K
732
K
J
732
85
7
P
I
7
T
761
7
p
O
732
N
32
J
732
N
M
732
M
L
732
L
i 1
K
732
1
INTERPOLATION BY NEWTON-GREGORY DIFFERENCE FORMULA
223
1 . (continued)
A 5 f (a + w) to J; J = A 6 f (a)
x(x - l)(x - 2)(x - 3)(x - 4)/4! A^a) to I
x(x - l)(x - 2)(x - 3)(x - 4)(x - 5)/6! to MC
A 6 f(a) to MP
product to I
OUT
IN
MISC.
K
J
32
I
7
U
761
(7)
J
7
I
7
224
SUBTABULATION
/<\ t* ~ +„wi„ ^-^0.4-0 n*,Arm n «inac r,t a ■FiineHon tnr> a certain interval of the argument, the process
~* . n i A1I ioH nn the Trainee nt the fimpHnn fnr n smaller interval of the argument is called sub-
tabulation.
(2) Subtabulation is carried out by differencing the given function, then either interpolating on these
differences for the intervening functions or determining a new difference table for the smaller
tabular interval from which to build the functions.
(3) If interpolation is to be used, the selection of a particular formula should be determined by the
following considerations:
(a) formulae which proceed to constant differences are exact,
(b) formulae which stop short of constant differences are not exact, but are approximate,
(c) approximate formulae terminating in the same difference are identical,
(d) approximate formulae terminating in distinct differences of the same order are not iden-
tical,
(e) central difference formulae terminating in a mean difference of order r are more exact
than formulae which terminate in a single difference of order r.
(4) For purposes of machine computation, the central difference formulae are usually more con-
venient. In particular, to subtabulate to tenths, the Newton-Bessel central difference formula
is well adapted to machine computation. See note (6) of the previous section.
If y(x + d) is the desired value of the function (0 < d < h and h = x - x^ _ ^)
y(x + d) = A (y Q + y ± ) + A^ + A 2 (a y_j_ + a y Q )
+ A 3 A 3 y_i + A 4< A4 y-2 + A Vi) + V 5y -2
+ A 6 (A 6 y_, + A 6 y_ 2 ) + A^y^ + Ag(A 8 y_ 4 + A 8 y_ 3 ) + ...
This form of the Newton-Bessel formula has the following advantages:
(a) the A- are short, terminating decimal fractions, thus reducing multiplication time and
eliminating errors arising from non-terminating coefficients,
(b) the values of the function for d/h = 0.6, 0.7, 0.8, 0.9 can be evaluated directly from the
computations for d/h = 0.4, 0.3, 0J2, 0.1, respectively, by appropriate reversals of sign,
thus almost halving the number of multiplications required,
(c) every second term in the function is zero when the value of the function for the half interval
d/h = 0.5 is computed.
(5) The numerical values of the Aj , for i = through 8, are given in Table 1.
(6) The Newton-Bessel formula should never be used without a careful examination of the error
introduced by neglecting the remainder. For references on this, see Bibliography, Subtabu-
lation.
(7) The error due to the neglect of the remainder does not include the errors inherent in machine
computation; e.g., cutting off digits in products. These errors must be evaluated for the par-
ticular problem.
225
SUBTABULATION
(8) Table 2 gives an example of the high accuracy which can be obtained using the Newton- Bessel
formula as given in note (4). In Table 2 the correct values of the function are given to 23
places of decimals, eighth differences were used, ten values of the function from 7.94 to 8.04
were used to subtabulate. The maximum error is but a few units in the 23rd decimal place.
TABLE 1
d/h
0.1
0.2
0.3
A
0.5
0.5
0.5
A l
-0.4
-0.3
-0.2
A 2
-0.022 5
-0.04
-0.052 5
A 3
0.006
0.008
0.007
A 4
0.003 918 75
0.007 2
0.009 668 75
A 5
-0.000 627
-0.000 864
-0.000 773 5
A 6
-0.000 795 506 25
-0.001 478 4
-0.002 001 431 25
A 7
0.000 090 915
0.000 126 72
0.000 114 367 5
A 8
0.000 171744 117 187 5
0.000 321 024
0.000 436 383 492 187 5
d/h
0.4
0.5
A
0.5
0.5
A l
-0.1
The A i5 i odd, equal zero for d/h = 0.5 .
A 2
-0.06
-0.062 5
A 3
0.004
A 4
0.011 2
0.011 718 75
A 5
-0.000 448
A 6
-0.002 329 6
-0.002 441 406 25
A 7
0.000 066 56
A 8
0.000 509 184
0.000 534 057 617 187 5
d/h = 0.6
The A 2k , k = 0, 1, 2, 3, 4, are identical with the corresponding values for d/h = 0.4 .
The A 2k + 1 ,k = 0, 1,2,3, are the negatives of the corresponding values for d/h = 0.4 .
d/h = 0.7
The A^, k = 0,l,2,3,4, are identical with the corresponding values for d/h = 0.3 .
The A 2k +1 ,k = 0, 1,2,3, are the negatives of the corresponding values for d/h = 0.3 .
d/h = 0.8
The A 2k' k = °' 1 » 2 ' 3 ' 4 ' are identical with the corresponding values for d/h = 0.2 .
The A 2k +1 ,k = 0, 1,2, 3, are the negatives of the corresponding values for d/h = 0.2 .
d/h = 0.9
The A 2k , k = 0, 1, 2, 3, 4, are identical with the corresponding values for d/h = 0.1 .
The A 2k A , k = 0, 1, 2, 3, are the negatives of the corresponding values for d/h = 0.1 .
226
CODING
TABLE 2
X
Correct Value of f(x)
Subtabulated Values of f (x)
7.980
7.981
7.982
7.983
7.984
1.763 147 388 660 678 723 1763
1.760 829 249 550 966 677 1468
1.758 509 640 161 486 144 7192
1.756 188 562 959 490 626 2892
1.753 866 020 413 355 311 2638
1.763 147 388 660 678 723 1763
1.760 829 249 550 966 677 1464
1.758 509 640 161 486 144 7188
1.756 188 562 959 490 626 2887
1.753 866 020 413 355 311 2633
7.985
7.986
7.987
7.988
7.989
1.751 542 014 992 574 599 4059
1.749 216 549 167 759 621 3753
1.746 889 625 410 635 758 4682
1.744 561 246 194 040 161 5585
1.742 231 413 991 919 269 2417
1.751 542 014 992 574 599 4057
1.749 216 549 167 759 621 3753
1.746 889 625 410 635 758 4683
1.744 561246 194 040 1615586
1.742 231 413 991 919 269 2418
227
INVERSE INTERPOLATION
(1) The values of an argument in arithmetical sequence and the corresponding values of a function
are given in tabular form. Inverse interpolation is the process of finding the value of the argu-
ment corresponding to a value of the function intermediate between two tabular values.
(2) The inversion of a functional table may conveniently be accomplished by iteration. One of sev-
eral iterative procedures is the following:
Let f(x) be a function tabulated for equal intervals of x. It is desired to retabulate this function
for equal intervals h of the variable y.
Assume that
,-1
x -2 s f wo " 2h)
and
x -l = f (y " h)
are two values of x previously found to correspond to (y n - 2h) and (y n - h). It is required to
find ° °
x n - f W •
(1)
A first approximation xi 1 ' to x n may be found from
x n^ = x _i + kn
where
k =
- x
• (2)
A second approximation x^' to x Q may be found by first computing
yd
(1)
= *N 1) ]
by direct interpolation. If a polynomial interpolation tape for use in direct interpolation is not
available, difference interpolation may be used here. Then
oo L o o J
Successively better approximations to x Q may be found by the repeated application of the last
two equations .
1. In the following example, the tape for direct interpolation is on interpolator III. Switch P
ita;
contains 1/h and y Q is in ctr. A. Ctr. C contains x_j and ctr. D contains x „. Ctrs. B,
E, F and G are available for computation of x ( 2 ). "
reset ctr. E
x to ctr. E
- x , to ctr. E; E = kh
OUT
IN
MISC.
E
E
7
C
E
7
D
E
732
Continued on next page
228
CODING
1.
^continued;
kh to MC
x_j to E; E = xi 1 )
reset ctr. F
1/h to MP
reset ctr. B
reset ctr. G
y„ to ctr. G
u
kh/h to ctr. F; F = k
f**srt v'- / f.-v iritc-rvrOai-.-.T* TTT QnH ernrr
™,to W (D_ *
1(1)1
ro j
ctr. B = y W
k to MC
(1)
- Yg to ctr. G; G = y Q - y Q
y Q - yW to MP
(1)
[>o->F]
to ctr. E; E = x
«*<*>
f ■
OUT
IN
!
MISC.
E
761
7
C
E
7
F
F
P
7
B
B
7
G
G
7
A
G
F
7
Hi
-TCK/IO
lUlIU
62
841
E
763
B
73
7
F
761
7
Ib
G j (7)32
G
(7)
E
7
(3) The tabular interval h of the function must be examined in order to determine the rapidity of
convergence before using this iterative process.
229
CARD FEEDS
(1) Before a problem involving card feeding is started, the feeds must be coupled to the machine.
They should be uncoupled when the problem does not involve card feeding.
(2) Cards are fed under an automatic control which will light a red light and stop the machine if the
cards run out, or if a card jam occurs. In order to use the card feed automatic safety control,
the switch on the card feed control panel must be thrown to the On position. When cards run
out, this switch must be thrown to the Off position in order to restart the machine.
(3) Card feeds may only be used to read into counters, not into functional units.
(4) The read-out of a number from a card feed may not be inverted. Negative numbers should be
punched as complements on nine.
(5) By plugging, numbers may be shifted to the right or left. If numbers are shifted to the left,
negative numbers should either be punched as complements on 10 or sufficient nines should be
plugged to the right. If numbers are shifted to the right, negative numbers require sufficient
nines plugged to the left. Plugging from any of the eighty card columns into any buss column is
possible. See Plugging Instructions.
(6) The card feeds may not be used in interposed operations during multiplication or division.
(7) If a control tape is coded to use card feed I, card feed II may be used by throwing the card feed
reverse switch. A similar comment holds for card feed II. The plugging is not carried over
by the switch.
(8) It is frequently necessary to check decks of cards to see that a certain group is used in a cer-
tain run, to see that cards are in their proper order and that cards from the two feeds are
properly paired or grouped. Serial numbers are used to denote the order of groups of cards.
Classification numbers usually follow serial numbers and denote the order of cards within the
group. If classification and serial numbers are punched in the cards, the classification numbers
may be checked through the automatic check counter. The serial numbers may be checked
against a value tape, an accumulation counter or another deck of cards.
(9) All decks of cards should be clearly labeled with the run in which they are to be used, the feed
in which they are to be placed and necessary information about their classification and serial
numbers.
1. Read out of card feed I into ctr. A.
2. Read out of card feed II into ctr. A.
3. Read out of card feed I into print ctr. I and print.
4. Read out of card feed II into punch ctr. and punch.
OUT
IN
MISC.
A
7632
A
76321
7432
632
752
7
753
6321
75
230
CODING
5. Read successive cards out of card feed I into print ctr. I
and print.
OUT
IN
MISC.
j~tO&
632
752
6
7432
632
752
6
(10) If necessary, the blank Out column of the card feed coding may be used to select a value tape
from which the value is read on the next line, or to turn on or off typewriters.
6. Read out of card feed I into ctr. A. Select the value tape
on interpolator I and read the value to ctr. B and step the
tape.
OUT
IN
MISC.
85
A
7632
B
753
7. Read out of card feed I into ctr. A. Turn on typewriter II.
871
A
7632
231
CARD PUNCH
(1) Before a problem involving punching is started, the punch cable connection must be closed.
This connection should be open when the problem does not involve punching to allow for manual
punching.
(2) Cards are fed into the punch under an automatic control such that lack of a card in punching
position will automatically stop the machine. This control operates with the codes 753 in the
In column and 51 in the Miscellaneous column, stopping the machine on the line following these
codes. If a card jam occurs, the direct current should be turned off and a card placed in punch-
ing position. The machine may then be started and the computation continued. Since this control
may stop the machine, the codes 753 in the In column and 51 in the Miscellaneous column must
not be interposed in multiplication or division.
(3) Numbers may be shifted to the right or left by suitable plugging. See Plugging Instructions.
(4) Negative numbers are punched as complements on nine.
(5) Since the punch counter has a complete set of carry controls, including end around carry,
quantities may be accumulated in it. It may be read into as into any storage counter except
that its read-in code is automatic, must not be followed by a 7 in the Miscellaneous column and
may be interposed in multiplication or division only when the coding is specially arranged.
(6) If a half pick-up is desired on values punched in cards, see Multiple In-Out Counter.
(7) Two punching operations are available. In the first, the punching operation is completed before
the machine starts the next operation, and in the second, the machine starts the next operation
as soon as punching is initiated.
(8) Ten cycles for punching must intervene between the start of one punching operation and the in-
itiation of another. Hence if it is necessary to perform a succession of punching operations,
the "punch and complete punching" code must be used.
(9) In the operating instructions of any problem it should be stated how cards punched are to be
labeled and stored.
1. Read the quantity in sw. or ctr. A into punch ctr. If no card
is in punching position the machine will stop on the next
line of coding.
2. Read minus the quantity in sw. (except IVS) or ctr. A into
the punch ctr.
OUT
IN
MISC.
A
753
A
753
32
3. Read minus IVS to the punch ctr.
8431
753
21
4. Punch out the number lying in the punch ctr. Start next
operation before punching is completed.
or
5
75
5 . Punch out the number lying in the punch ctr . and complete
punching before starting next operation.
51
232
CODING
6. Reset the punch ctr.
7. Read out of the punch ctr.
8. Punch out the quantity lying in sw. or ctr. A.
9. Accumulate the quantities lying in sws. or ctrs. A, B, C
and D and punch out the sum.
10. Punch successively the quantities lying in sws. or ctrs,
A and B.
OUT
IN
MISC.
843
863
A
753
75
A
753
B
753
C
753
D
753
75
n.
1753
1 1
51
B
753
75
fim ThP blank Out and In column of the line of coding initiating punching may be used to code any
( ' ooerato not requiring an operational code in the Miscellaneous column. The code which in-
^^SiX^S* be combined with the invert code or any other operational code in
;^«SS^«rSmnn. That is, the 5 or 75 in the Miscellaneous column initialing punching
may" beTnse'rted in any Miscellaneous column not already containing an operational coae uuier
than 7.
(U) The blank Miscellaneous column of the line of coding reading into the punch counter (if not
( ] Led for an invert or other such operational code), may be used to code the stepping of a tape
on an interpolator.
11. Print and punch the quantity in sw. or ctr. A. Type-
writer I.
OUT
IN
MISC.
A
753
A
7432
752
75
CARD PUNCH
233
12. Multiply sw. or ctr. A by sw. or ctr. B. Deliver the
product to ctr. C. Punch out the quantity standing in
the punch ctr. Turn off typewriter I.
or
or
13. Multiply minus sw. (except IVS) or ctr. A. by the ab-
solute value of ctr. B. Deliver the product to ctr. C
and punch out the quantity in the punch ctr. Turn on
typewriter I.
14. Multiply minus sw. (except IVS) or ctr. A. by sw. or
ctr. B. Deliver the product to ctr. C, punch out the
quantity in the punch ctr. and step and read the value
from the tape on interpolator I to ctr. D. Turn on
typewriter II .
15. Punch the quantity in sw. or ctr. A, print it with half
pick-up on typewriter I, multiply minus sw. (except
IVS) or ctr. B by ctr. A, deliver the product to ctr. C,
step the value tape on interpolator II three times, and
read the value to ctr. D.
OUT
IN
MISC.
A
761
5
B
8732
C
7
A
761
B
5
8732
C
7
A
761
B
8732
C
75
A
761
32
B
2
872
C
75
A
761
32
B
5
85
C
753
871
D
7
A
753
531
B
761
32
A
7432
531
76543
531
752
5
851
C
7
D
7
(12) In order to check the values punched in cards, summations of the quantities punched may be
employed. Suppose f(x n ) is computed and punched, the quantities f (x ) are accumulated in the
234
CODING
machine and the summations printed out.
The difference
k k - 1
o l o x . *
is computed and subjected to a check procedure.
The cards are later summed on a tabulator or fed to the machine and summed. If the inde-
pendent summations are compared, this process insures that f (x^) has been correctly punched.
Note that if the check is made directly on f(xj c ) as computed, the cards are not checked since
the read-outs to the accumulation and punch counter could be incorrect.
(13) Cards may be punched containing a function in the first n card columns and a code number in
the last columns of the card. After the first n columns are punched, a duplicating card and
skip bar control the punch. The punch counter resets and the code number is added into the
punch counter. The code number is then punched in the columns fixed by the skip bar.
16. Punch the 24 columns of the function f(x) standing in ctr. A in card columns 1-24. Punch
the code number accumulated in ctr. E from ctrs. B, C and D in card columns 70, 73, 74,
75, 76 and 79. The duplicating card contains an R in column 25. The punch is plugged as
shown below.
PUNCH MAGNETS
/
10
9 9 8 9
o o
o o
V
2A
;%
25 30
loooo 0000
2B
» • J -»| • ' •
45
50
~65 \ 7 9*C
o o o o ^« • // ^-»
COMP MAG OR CTR
4A
4B
15
20
a a
35
55
V
40
o do o
75
TOT EXIT 0R| MS
6A
o o
40 s !
60
o o
80
IN
6B/
yj,
oooo 0000 oooo
reset ctr. E
accumulate the code number in ctr. E
OUT
IN
MISC.
E
E
7
B
E
7
c
E
7
Continued on next page
CARD PUNCH
235
16. (continued)
f(x) to punch ctr.
punch out f (x)
code number to punch ctr.
punch out code number
OUT
IN
MISC.
D
E
7
A
753
51
£
753
51
236
PRINTING
(1) The decimal point, vertical spacing, horizontal spacing, half pick-up and argument control all
require plugging e See Plugging Instructions.
(2) The typewriters should be turned on at least two cycles before they are required to print. The
typewriters may be turned off as soon as printing operations are completed; i.e„ 20 to 23
cycles after the initiation of the last print or immediately after a "print and complete printing"
code.
(3) There are three parts of the printing operation, the read-in to the print counters, the half pick-
up which may be used or not as desired and the initiation of the printing operation.
(4) Negative numbers may be printed as such or as complements on nine if the print complement
switch is thrown.
(5) Since the print counters have complete sets of carry controls including end around carry cir-
it— *.:xt~~ __„v^ .^....v.ln^Aj i~ fViQtx Tlian wiottKo t-oq/I ltitn oe i«+r» QnwoMrooro pnnntor
UUitS, uudlluilCB ma.y uc a^vuuiuiaicu m uicui, iixcjr uiajuc iwo** i*i»i> &u luw o.»»jr u »v>i>gc w~— - ~-
except their read-in codes are automatic and must not be followed by a 7 in the Miscellaneous
column.
(6) Two printing operations are available. In the first, the printing operation is completed before
the machine starts the next operation, and in the second, the machine starts the next operation
as soon as printing is initiated.
(7) The operation "print and complete printing" must not be interposed in multiplication or division.
(8) Approximately 23 cycles for printing must intervene between the start of one printing operation
and the beginning of another. Hence if it is necessary to perform a succession of printing
operations, the "print and complete printing" code must be used. See Timing.
(9) The half pick-up may be used if a number is to be rounded off to fewer digits than the machine
capacity. Its effect is to add one in the lowest order column retained if the next lower column
contains five or more. Actually the half pick-up adds or subtracts five in the column to which
it is plugged, in the print counter for which it is coded, according as the number in the print
counter is positive or negative. A half pick-up may also be added in from a switch under con-
trol of counter 70. See Choice Counter.
(10) If a control tape is coded to use print counter I and typewriter I, print counter II and typewriter
II may be used by throwing one of the typewriter reverse switches. A similar comment holds
for typewriter II. Note that this does not change over the half pick-up which is not reversed
and continues to add into the print counter for which it is coded .
(11) Numbers from print counter I may only be printed on typewriter I. Numbers from print counter
II may only be printed on typewriter II.
(12) There is available a special control on printing, the "argument control", which will cause the
typewriter not to print zeros to the right of the point to which it is plugged. This code, an 87
in the Out column, is placed on the line of coding initiating printing.
1 . Turn on typewriter II .
2. Turn on typewriter I.
OUT
IN
MISC.
871
872
1
PRINTING
237
3. Turn off typewriter n.
4. Turn off typewriter I.
OUT
IN
MISC.
8731
8732
5. Read the quantity in sw. or ctr. A to print ctr. I.
A
7432
6. Read minus the quantity in sw. (except IVS) or ctr. A
to print ctr. I.
A
7432
32
7. Read minus the quantity in IVS to print ctr. I.
8431
7432
21
8. Read the quantity in sw. or ctr. A to print ctr. II,
A
74321
9. Read minus the quantity in sw. (except IVS) or ctr. A
to print ctr. n.
A
74321
32
10. Reset print ctr. I. Cannot be used while either typewriter
is printing.
842
11. Reset print ctr. II. Cannot be used while either typewriter
is printing.
8421
12. Read out of print ctr. I.
862
13. Read out of print ctr. n.
8621
14. Multiply sw. or ctr. A by sw. or ctr. B and deliver the
product to print ctr. I.
A
761
B
7432
15. Print the quantity in print ctr. I on typewriter I and com-
plete printing before starting other operations.
752
6
238
CODING
16. Print the quantity in print ctr. n on typewriter II and com-
plete printing before starting other operations.
I 1
OUT
IN
MISC.
7521
6
17. Print the quantity in print ctr. I on typewriter I and
start other operations.
752
7
18. Print the quantity in print ctr. II on typewriter II and
start other operations.
7521
7
19. Read the quantity in sw, or ctr = A to print ctr, I and
print on typewriter I.
A
7432
752
7
20. Read minus the quantity in sw. (except IVS) or ctr. A
to print ctr. n and print on typewriter II.
A
74321
32
7521
7
21. Print the quantity in print ctr. I on typewriter I omit-
ting zeros to the right.
87
752
7
22. Print the quantity in print ctr. II on typewriter n
omitting zeros to the right.
! 1 1 1
i87 17521 1 7 I
I I ' I I
23. Add half pick-up to print ctr. I.
76543
24. Add half pick-up to print ctr. II.
765431 1
25. Print the quantity in sw. or ctr. A with half nlck-u
on typewriter I.
A
7432
76543
752
7
26. Print minus the quantity in sw. (except IVS) or ctr. A
with half pick-up on typewriter II.
A
74321
32
765431
7521
7
239
PRINTING
27. Multiply sw. or ctr. A by sw. or ctr. B. Deliver the
product to print ctr. I and print.
OUT
IN
MISC.
A
761
B
7432
752
7
28. Step and read the value from the tape on interpolator I
to print ctr. I and print.
85
753
7432
752
7
29. Print successively the quantities lying in sws. or ctrs. A
and B on typewriter I.
A
7432
752
6
B
7432
752
7
30. Print the quantity lying in sw. or ctr. A on typewriter I
and the quantity in sw. or ctr. B on typewriter II.
A
7432
752
6
B
74321
7521
7
31. Multiply sw. or ctr. A by sw. or ctr. B. Deliver the
product to ctr. C and print B on typewriter I with
half pick-up.
A
761
B
7432
76543
752
C
7
(13) The blank Miscellaneous column of the lines of coding reading into the print counter (if not
used for an invert or other such operational code), reading in the half pick-up, or initiating
printing, may be used for punching or stepping an interpolator.
(H) i^L^t In i COl r n ? tt f lin f ° f ° 0ding reading in the haK P ick ~ u P or initiating printing may
be used to select a value tape from which the value is read on the next line.
240
CODING
32. Print the quantity in sw. or ctr. A with half pick-up. Step
the tape on interpolator HI back three times and read the
value to ctr. B.
33. Multiply minus ctr. A by the value from the tape on in-
terpolator n after stepping ahead once, deliver the
product to ctr. C, print the quantity in sw. or ctr. B with
half pick-up, and punch out the quantity in the punch ctr.
34. Punch and print with half pick-up the absolute value of
the quantity in ctr. A on typewriter I, multiply it by minus
sw. or ctr. B and deliver the product to ctr. C.
OUT
IN
MISC.
A
7432
542
76543
542
852
752
7542
B
7
A
761
732
B
7432
5
OC1
76543
531
752
C
7
A
753
2
A
761
72
A
7432
2
76543
c
•J
B
752
32
C
7
(15) Printed data may be checked by printing quantities on both typewriters or by simultaneously
printing and punching and later checking the punched cards against the printed results.
(16) Quantities or groups of quantities may be printed simultaneously on both typewriters. This
requires special wiring in the machine and that the typewriters be plugged identically, except
for the read-out control. It is necessary to read into both print counters, but only one code to
initiate printing need be used, since the wiring "gangs" the codes 752 and 7521.
(17) As an added precaution for greater accuracy of the typewriters, half-time printing may be used.
For half-time printing omy every ouier cuiuum scictuuu Hi » & »«w .- *—&&— — - -• o~ -- — - —
print counter read-out. The intervening plughubs are left blank or may be filled by the argu-
ment control, the decimal point or spaces if desired. This may be of particular advantage when
printing on both typewriters at the same time, if the column selection plughubs of the two type-
writers are plugged alternately and provided that the number of digits in each printed quantity
is small enough. See Plugging Instructions.
(18) When there are manyprints in a computation, so that it is desired to print as rapidly as possible,
the code 76 in the Miscellaneous column may be used instead of the usual 7 or 6 with 752 or
7521. This will allow other operations to be interposed during the printing time, but does not
permit a print to be initiated until the previous print is completed. As in other interposed oper-
ations, the automatic (7 in the Miscellaneous column) must be omitted from the last interposed
line.
241
INTERPOSITION OF MACHINE STOPS
(1) It is possible under specialized codings for the machine to choose the time at which certain
operations will be performed. This possibility of a choice is inherent in the nature of the auto-
matic codes controlling the functional units. In particular, the choice of the time at which the
product is read out makes it possible to interpose in multiplication and division certain codes
which may stop the machine.
(2) The check procedure and the read-in to the punch counter may be interposed in multiplication
or division only when the coding is specially arranged. This special coding prevents the loss
of the multiplication or division if the check fails or if there is no card in punching position.
The saving of time is but two cycles, but if checking and punching are frequent operations in a
tape, the time saved may become proportionately large per revolution. The coding must be
used with extreme caution.
(3) It is necessary to code the read-in to the punch counter or the check procedure immediately
before the read-out of the product and to duplicate the product read-out. The first coding of
the product-out must not have a 7 code in the Miscellaneous column. If the procedure fails,
the machine stops on the first product-out. The automatic from the completed multiplication
will cause the sequence mechanism to read the first product-out line. The product will be de-
livered to the designated storage counter. The sequence mechanism will step to the next line
of coding and stop, since there was no Miscellaneous 7 on the product-out line. It should be
noted that if there were a Miscellaneous 7 on the product-out line, the machine would continue
operation as if the check had not failed. If the check or punch read-in does not fail, the auto-
matic from the procedure will cause the sequence mechanism to read the first product-out as
if it were the last line of interposed coding and step to the next line. No transfer will take place
since there is no code in the Out column. The automatic from the completed multiplication will
cause the sequence mechanism to read the second product-out line which has a 7 in the Miscel-
laneous column, the product will be delivered to the designated storage counter and the machine
will continue operation.
1.
Multiply the quantity in sw. or ctr. A by the quantity in
sw. or ctr. B and deliver the product to ctr. C. Interpose
a read-in from ctr. D to the punch ctr. Lines reading
(blank, blank, 7) or (blank, blank, blank) may be used for
interposed operations.
OUT
IN
MISC.
A
761
7
7
B
7
7
7
D
753
C
C
7
2.
Multiply the quantity in sw. or ctr. A by the quantity in
sw. or ctr. B and deliver the product to ctr. C. Interpose
761
Continued on next page
242
CODING
2 . (continueu;
a check of the quantity in ctr. D against the tolerance in
sw. W during the multiplication. Lines reading (blank,
blank, 7) or (blank, blank, 64) may be used for interposed
operations .
! OUT '
IN 1
MISC.
7
74
74
B
7
SW
74
7
D
74
71
64
C
C
7
3. Multiply the quantity in sw. or ctr. A by the quantity in
sw. or ctr. B and deliver the product to ctr. C. Interpose
a "ganged" print from ctrs. B and E and a check of the
quantity in ctr. D against the tolerance in sw. W during
the multiplication.
A
761
7
74
74
7
SW
74
B
74321
E
7432
!
D
74
71
i
1
752
64
1
C
C
7
(4) If both the read-in to the punch counter and the check procedure are to be interposed, there must
i 4. i *■ *™~ „™,_„ Q *.r. Hicritc in oithpr thp nHd or the even columns of the multiplier. The
product-out line of coding must appear three times. First, immediately after^the check pro-
cedure, it appears with a 7 in the Miscellaneous column; secondly, immediately after the rcad=m
to the punch counter, it appears without a 7 in the Miscellaneous column; thirdly, in the following
line, it appears with a 7 in the Miscellaneous column.
If the check procedure fails, the machine will stop on the first product-out line. The automatic
from the completed multiplication will signal the sequence mechanism to read this first product-
out line and step to the next. The product will be delivered to the designated storage counter.
The 7 in the Miscellaneous column will order the sequence mechanism to read the next line of
coding and step to the next. There will be a read-in to the punch counter. The automatic from
the punch counter read-in will order the sequence mechanism to read the next line. This line
(blank, C, blank) will effect no transfer and the sequence control will remain on the last line of
coding.
243
INTERPOSITION OF MACHINE STOPS
(5)
If there is no card in punching position, the machine will stop on the second product-out line.
The automatic from the completed multiplication will signal the sequence mechanism to read
the second product-out line and step. The product will be delivered to the designated storage
counter and the machine will remain on the last line of coding.
If the check fails and there is no card in punching position, the machine will stop on the first
product-out line. The automatic from the completed multiplication will signal the sequence
mechanism to read the first product-out line and step. The product will be delivered to the
designated storage counter. The 7 in the Miscellaneous column will order the sequence mecha-
nism to read the next line of coding and step. Since there is no card in punching position, the
sequence mechanism will remain on the second product-out line.
If neither the punch counter read-in nor the check procedure fails, the automatic from the
check will cause the sequence mechanism to read the first product-out line as if it were merely
a line of interposed coding. No transfer will take place, since there is no code in the Out
column. The 7 in the Miscellaneous column will order the sequence mechanism to read the
next line of coding and step. There will be a read-in to the punch counter. The sequence mecha-
nism will read the second product-out as if it were the last line of interposed coding. No
transfer will take place since there is no code in the Out column. The automatic from the
completed multiplication will cause the machine to read the third product-out line. The product
will be delivered to the designated storage counter. The machine will continue operation.
Similar codings may be applied to division. There will of course be more interposed lines
during the division, and the check or punch procedure will immediately precede the read-out of
the quotient.
4.
5.
Multiply the quantity in sw. or ctr. A by the quantity in
sw, or ctr. B and deliver the product to ctr. C. Interpose
a check of the quantity in ctr. E against the tolerance in
sw. W and a read-in from ctr. D to the punch ctr. Line
reading (blank, blank, 64) may be used for an interposed
operation.
Divide the quantity in ctr. A by the quantity in ctr. B
and deliver the quotient to ctr, C. Division must be
plugged to at least ten digits. Interpose a check of
the quantity in ctr. E against the tolerance in sw. W
OUT
IN
MISC.
A
761
7
74
74
7
SW
74
B
7
E
74
71
64 •
C
7
D
753
C
C
75
B
761
7
74
74
7
Continued on next page
244
CODING
and a read-in from ctr. D to the punch ctr. Lines reading
(blank, blank, 7) and (blank, blank, 64) may be used for
interposed operations.
OUT
IN
MISC,
SW
74
A
7
7
7
7
7
7
7
E
74
71
64
C
7
D
753
C
1
C
75
245
CHAPTER V
PLUGGING INSTRUCTIONS
"One deviates to the right, another to the left; the error is the same with all but it
deceives them in different ways." Horace.
Once the tapes necessary to the solution of a problem have been prepared, the appropriate
switches set and the plugging completed, the calculator may be started. The machine will then con-
tinue in operation, hour after hour, completely checking its own results until either the problem has
been solved or until a breakdown occurs. Experience has shown that the calculator will operate
approximately ninety percent of the time without failure of any kind, and on occasion has run as long
as four weeks without interruption. At such times it is necessary for the operator only to exercise
minor supervision such as checking the bearing temperatures, keeping the typewriters supplied with
paper and the feeds with cards. However, the accuracy of all computed results is dependent not only
upon the accurate operation of the calculator itself but also upon the accuracy with which the manual
adjustments were made prior to starting the problem. Herein lies the only opportunity for error
which is not automatically checked by the machine itself. The calculator is far more nearly infallible
than the personnel in charge of its operation. The setting of the switches and the plugging of the
functional units provide the two possible sources of human error. It cannot be too strongly emphasized
that these two operations must be carried out with the greatest of care and thoroughly checked before
a problem is started. For example, if two neighboring wires in the typewriter plugging are inter-
changed, two digits in the printed results will be interchanged. The entire computation will have been
automatically checked by the calculator, but the results will be incorrectly printed. If two card feed
plugwires are interchanged, the calculator will compute on incorrect input data, check its computation
and the error will not be detected. It is essential therefore that the plugging be checked by reading
in known values, such as diagonal numbers, and printing them out before a computation is begun.
The plugging of a particular unit, though tedious, is not difficult once the underlying principles
and the labeling of the plugboards are understood. In order to simplify the plugging diagrams, a
wiring convention will be employed. Whenever n successive plughubs in any one row of the plug-
246
PLUGGING INSTRUCTIONS
board are to be plugged in one to one correspondence with n other plughubs in another row, the n
plugwires will be represented by a single connection as shown in the following diagram.
o o o o o •— •
ooooo
o o o • • •••oo
Actual wiring
o o o
o o
Convention
For convenient reference the plugging instructions have been divided into sections correspond-
ing to the various units of the machine and to the sections of the chapter on coding.
1
Section
Page
Section
Page
Multiplication
247
Sine Unit
258
Division
249
Interpolators
262
Logarithm In-Out Counter
251
Card Feeds
272
Sine In-Out Counter
252
Card Punch
274
Logarithm Unit
254
Printing
275
Exponential Unit
256
Sample Plugging
281
247
MULTIPLICATION
(1) The multiply unit requires plugging for the read-out of the PQ counter into the buss.
(2) If the operating decimal point of the machine lies between columns n and n + 1, the decimal
point of the PQ counter lies between columns 2n and 2n + 1. From the PQ counter, 23 columns
and the algebraic sign are read into the buss (P-OUT plughubs). The P-OUT plughubs are so
plugged that the decimal point of the quantity standing in the PQ counter is shifted to conform
with the operating decimal point; i.e.,
2n + 1st plughub of PQ to n + 1st plughub of P-OUT,
2nth plughub of PQ to nth plughub of P-OUT,
sign plughub of PQ to 24th plughub of P-OUT.
The plugging is continued to the right and left until the P-OUT plughubs are filled.
(3) The PQ counter plughubs lie in rows 2 and 3 of the MP-DIV plugboard. The P-OUT plughubs
lie in the 4th row of the same board. The sign plughub of the PQ counter is the 24th plughub in
the 3rd row.
1. Plug the multiply unit for operating with the decimal point between columns 15 and 16.
Row 2
25
Row 3 o
^sign
20
ooooo ooooo ooooo PQ CTR
15 10 5
Row 4 o
oooo ooooo
46 45
40
35
30
24
20
15
10
PQ CTR
P-OUT
(4) The omission of plugging to some of the low-order P-OUT plughubs increases the speed of com-
putation at the expense of accuracy, since fewer non-zero digits are carried to the next step in
the computation.
2. The operating decimal point lies between columns 19 and 20. Plug the multiply unit to read
no more than twelve decimal places from the PQ counter.
Row 2 ooooo ooooo ooooo ooooo ooooo PQ CTR
25 20 15 10 5
^sign
Row 3 ofooo o o o •-
46 45
Row 4 o •
40
35
30
o PQ CTR.
24
20
15
10
oo ooooo P-OUT
5
(5) For high accuracy computation, the operating decimal point is assumed to lie between columns
23 and 24.
248
PLUGGING INSTRUCTIONS
3 "Diner flip nrmlHttlv unif fnr hiorh af»f»nrar»ty pnTvmn+afripTi
Row 2
Row 3
Row 4
ooo
25
^ sign
o • o o
o 1 •— •-
20
o o o o o
15
o o o o o
10
5
46 45
40
35
30
JT
PQ CTR.
PQ CTR.
P-OUT
24
20
15
10
(6) Table 1 shows the necessary plugging for the read-out from the PQ counter to the buss (P-OUT
plughubs) for each position of the operating decimal point. The number at the top of each column
refers to the P-OUT plughub. The numbers in the body of the table refer to the PQ counter plug-
hubs. Note that the sign plughub of the PQ counter is connected to the 24th P-OUT plughub.
TABLE 1
I
MULTIPLICATION
: PQ COUNTER TO P-OUT
P-
OUT COLUMNS
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
1/0
S
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
2/1
S
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
3/2
s
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
4/3
s
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
5/4
s
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
6/5
s
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
g ty»
s
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
S 8/7
s
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
S 9/8
s
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
*** xu/»
s
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
13 11/10
s
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
S 12/11
s
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
8 13/12
s
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
Q 14/13
s
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
g> 15/14
§ 16/15
s
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
s
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
S "/is
s
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
§ 18/17
u 19/18
s
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
s
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
20 /1Q
Q
dO
ill
An
tQ
ia
•in
9r
m
*A
<i<*
19
n
in
9Q
90
97
9ft
on
9A
ot
99
91
9r» 1
21/20
s
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
ZZ/2I
s
44
43
42
41
4U
ay
m
37
3b
3b
34
33
32
31
3U
zy
28
27
26
25
24
23
22
23/22
s
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
24/23
s
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
249
DIVISION
(1) Division requires:
A. plugging for the number of comparisons to be made during the dividing operation
B - ir^e pirrxrr 1 ' o( shm to "- right ° £ the ™*-°«"^°*
in a dividing operation may vary from 1 to 24. Five orders of accuracy may be selected Tn tWs
? T h l n ? n " a c Utomatic operational codes in the Miscellaneous column The codes are assoc
ated with the 25th plughubs of rows 1, 3, 4, 5 and 6 of the MP-DIV plugboard
(2)
Code
643
6431
6432
64321
blank
25th plughub in row
6 minimum accuracy
4
3
1 maximum accuracy
^r 1 ^ 1 " ° f c ° m P ai l isons is controlled by the plughubs of the first row of the MP-DIV plug-
board The number of comparisons includes a first no go if such occurs This implies tffif
d secant digits are desired in the PQ counter, the dividing operation must b7p ugged f or
read-outTsTsed 0nS " ^ " C ° 1UmnS "* ^ ° Ut ° f the ^ counter ***** «J flow order
1. Plug the place limitations of division to provide 4, 9 and 15 significant digits in the PO
counter, using codes 643, 6431 and blank respectively. ^
Row 1
Row 2
^ code blank
oooo oooo
23 20
o o o o o
15
00000 00000 ooooo
code 64321
Row 3 ooooo ooooo ooooo
code 6432
Row 4*ooooo ooooo ooooo
-code 6431
Row 5
Row 6
oooo ooooo ooooo
• oooo
Ao
OOOOO
ooooo
ooooo
ooooo
- code 643
f ° ° oo ooooo ooooo ooooo
• oooo
ooooo
ooooo
ooooo
ooooo
ooooo
2 ' t P he U bll h nk P c^de Umitati ° n ° f diViSi ° n to P rovide " significant digits in the PQ counter, using
Row 1
•code blank
[oooo o •
23 20
ooo ooooo ooooo ooooo
15
10
250
PLUGGING INSTRUCTIONS
3. Plug tne piace nmiiauon ui uivisiuu tu piuviuc *» oigiunv.aui.uign.u x« ..»«, *. v& , o
the blank code.
^-code blank
Row lffOOO ooooo ooooo ooooo ooooo
U000 OOOOO uuuuu vj «j u « « vr
23 20 15 10 5
(3) The amount of shift to the right of the read-out of the quotient from the PQ counter to the buss
is controlled by a pair of manually set switches. These two dial switches, located to the right
of the sequence mechanism, are labeled "Divide N minus decimal". The switches must be set
to the value 22 - n, where the operating decimal point lies between columns n and n + 1. For
high accuracy computation, the switches must be set to 00.
251
LOGARITHM IN-OUT COUNTER
(1) The LIO counter has a pluggable read-out from the counter into the buss.
(2) The LIO-OUT plughubs lie in row 26 and the corresponding buss plughubs in row 25 of the
functional plugboard. The auxiliary nines, necessary in plugging for negative numbers, lie in
the ten plughubs of the right side of the bottom row of the board.
(3) The LIO counter may be used to shift quantities to the right or left; i.e., to multiply by a power
of ten.
1. Plug the LIO counter to shift quantities 5 columns to the left; i.e., to multiply by 10 .
-•-• • • • • • BUSS
c I
Row 25 o •
24
20
15
10
Row 26 o»ooo oo
24 20
15
10
o o o o o • • • • •
10 5
LIO-OUT
9's
Bottom Row
2. Plug the LIO counter to shift quantities 8 columns to the right; i.e., to multiply by 10
BUSS
-8
Row 25 o • <
24
Row 26 o • <
24
Bottom Row
20
15
10
20
15
-•— • ooo ooooo
10 5
o o
10
LIO-OUT
9's
(4) The LIO counter may be used to drop off digits from any quantity.
3. The operating decimal point lies between columns 15 and 16. Plug the LIO counter to read
out only the decimal part of a quantity.
Row 25 o • (
24
20
Row 26 o»ooo ooooo
24 20
Bottom Row
15
10
BUSS
LIO-OUT
15
10
o o 9*s
10
4. The first five columns of a quantity constitute a serial number. Plug the LIO counter to
drop off the serial number.
Row 25
Row 26
24
20
BUSS
15
10
24
20
15
10
ooooo LIO-OUT
5
Bottom Row
• • i • • ooooo 9's
10 5
252
SINE IN-OUT COUNTER
\±j xhe oxw cuuiiter nass a piuggaDie reaa-in, csiu-ijn 11, ana two pluggable reaa-outs, SIO-UUT l
and SIO-OUT II. The "85-1 FU" switch must be in the off position when the SIO counter is used
for any operation not a part of the sine computation.
(2) The SIO-IN II plughubs lie in row 32 and the corresponding buss plughubs in row 33 of the
functional plugboard. This read-in is associated with the automatic code 8741 in the In column.
(3) The SIO-OUT I plughubs lie in row 35 and the corresponding buss plughubs in row 34 of the
functional plugboard. This read-out is associated with the code 874 in the Out column.
(4) If negative quantities are to be routed via SIO-IN II and SIO-IN I, auxiliary nines must be sup-
plied from a switch under control of the choice counter.
(5) The SIO-OUT II plughubs lie in row 36 and the corresponding buss plughubs in row 37 of the
functional plugboard. The auxiliary nines, necessary in plugging for negative numbers, lie in
the ten plughubs of the left side of the bottom row of the board. This read-out is associated
with the code 84 in the Out column.
(6) If the "SIQ-QITT-2 Tpvert C.nntvn\" s-anffh i= in tho rm nnc iH nK s «*«*. 5« *k^ «m*j* «,o,„~.~ „,;n
pick up the plugged auxiliary nines and will invert the read-out of the plugged columns of SIO.
If the switch is in the off position, a nine in the 24th column will pick up the plugged auxiliary
nines but the read-out of the plugged columns of SIO will be direct.
(7) The SIO counter may be used to shift quantities to the right or left; i.e., to multiply by a power
of ten.
1. Plug SIO-IN II to shift positive quantities 2 columns to the left; i.e., to multiply by 100.
r*
Row 32 o /t • • • — > • • » • — •• •■>• — • • • • • » » « o o SIO-IN II
i
24 20 15 10
Row 33 o >• o o • — • • • • • — • •>•> < »«»«« • • • 9 • BUSS
24 20 15 10 5
2. Plug SIO-OUT I to shift positive quantities 3 columns to the right; i.e., to multiply by 10- 3 .
ROW o"x O S O O O 9 9 9 9 8" S S S 9 9
20 15
a e i i • >> » »■» BUSS
10 5
Row 35 O • • • • • • 9 9 9 •• ! «•• • m m m m » a n n n STO-mrr t
20 15 10 5
3. Plug SIO-OUT II to shift quantities 2 columns to the right; i.e., to multiply by 10" 2 .
Row 36
:c
24 20 15
Row 37
• • • • • — • • • o o SIO-OUT II
10 5
T
nM . • • • • • • • • • • BUSS
24 20 15 10 5
Bottom
Row o o 9J-9 o 00000
25 20
253
SINE IN-OUT COUNTER
(8) The SIO counter may be used to drop off digits from any quantity.
4. Plug SIO-OUT I to shift the 23rd column of a quantity to the 1st column of the buss. Plug
SIO-OUT II to shift columns 1-22 of a quantity one column to the left. This plugging is
used in high accuracy division.
Row 34 ooooo ooooo ooooo ooooo o o o o • BUSS
24 20 15 10 5
Row 35 ooioo ooooo ooooo ooooo ooooo SIO-OUT I
24 20 15 10 5
Row 36 ooo •• » » y . . . . » . . . . . SIO-OUT n
24 20 15 10 5
L2
Row 37 o o . BUSS
24 20 15 10 5
5. The operating decimal point lies between columns 15 and 16. Plug SIO-OUT I to read the
integral part of a positive quantity to the buss. Plug SIO-OUT II to read the decimal part
of a positive quantity to the buss.
Row 34 o o ••• • ••>• ooooo ooooo ooooo BUSS
24 r20 15 10 5
Row 35 o o • • • \ • 9 * ooooo ooooo ooooo SIO-OUT I
24 20 15 10 5
Row 36 ooooo ooooo • • m > m — • • • « t «»«»« SIO-OUT II
24 20 15 10
Row 37 ooooo ooooo
24 20 15 10
BUSS
254
LOGARITHM UNIT
1^ The logarithm unit requires:
A° plugging to read the logarithm from the LIO counter into the buss,
B. a switch setting used in the determination of the characteristic,
C. plugging to terminate division; see Division.
(2) At the end of the computation, the logarithm stands in the LIO counter with decimal point be-
tween columns 21 and 22. The LIO-OUT must be plugged to read the logarithm into the buss
with decimal point at the operating position.
(3)
The LIO-OUT plughubs lie in row 26 and the corresponding buss plughubs in row 25 of the
functional plugboard. The auxiliary nines, necessary if the logarithm has a negative charac-
teristic, lie in the ten plughubs of the right side of the bottom row of the board. Since only ten
such auxiliary nines are available, special provisions must be made for computing logarithms
.' « *u-«- -■s.i ■«■-- 'ci „„■»■:_,. /l n »;»nl nlonoo Sao CnAincr T.naarithm Unit.
(4) Table 2 shows the necessary plugging of LIO-OUT for each position of the operating decimal
point. The number at the top of each column refers to the buss piughub. The numbers in tne
body of the table refer to the LIO-OUT plughubs, except that "9" s" refers to any of the ten plug-
hubs at the right side of the bottom row of the functional plugboard.
TABLE 2
LOGARITHMS
LIO-OUT TO BUSS
1
BUSS COLUMNS
24
23
nn rt-t nr\ 1 Q
&£, lii. £i\l i-O
18
1 n i g i g 14
13 12
11 10
9
8
7
6
5
4
3
2 1
1/0
9/1
24
94
23
23 22
22 21
3/2
4/3
5/4
6/5
§ 7/6
2 8/7
S 9/8
°< 10/9
"i n / 10
.5 12/11
24
24
24
24
24
24
24
24
24
24
23
23
22
23
22
21
22
21
20
21 20
20 19
19 18
23
22
21
20
19
18 17
23
22
21
20
19
18
17 16
23
22
21
20
19
18
17
16 15
*
23
23 22
22
21
21
20
20
19
19
18
18
17
17
16
16
15
15 14
14 13
23
22 21
20
19
18
17
16
15
14
13 12
9b
9's 9b 9b 9's
9b
9b 9b 9b 9b
23 22
21 20
19
18
17
16
15
14
13
12 11
S 13/12
Q 1 A f\ 1
24
9's
9b 9b 9b 9's
9b
9b 9b 9b 23
22 '21
2U iy
ia
17
ID
10
it
10
14
JLX 1U
OA
Qlo
Qfc QVi QVi 9's
9<s
9b 9b 23 22
9b 23 22 21
21 20
20 19
19 18
18 17
17
16
16
15
15
14
14
13
13
12
12
11
11
10
10 9
9 8
c 15/14
% 16/15
% 17/16
g 18/17
19/18
20/19
21/20
22/21
23/22
24/23
24
9's
9b 9b 9's 9's
9b
24
9 b
9b 9b 9b 9ls
9b
23 22 21 20
19 18
17 16
15
14
13
12
11
10
9
8 7
24
9's
9's 9b 9's 9's
23
22 21 20 19
18 17
16 15
14
13
12
11
10
9
8
7 6
24
9's
9's 9's 9fe 23
22
21 20 19 18
17 16
15 14
13
12
11
10
9
8
'I
6 5
24
9's
9b 9b 23 22
21
20 19 18 17
16 15
14 13
12
11
10
9
8
7
b
5 4
24
9b
9b 23 22 21
20
19 18 17 16
15 14
13 12
11
10
9
8
7
b
b
4 3
24
9's
23 22 21 20
19
18 17 16 15
14 13
12 11
10
9
8
7
6
b
4
3 2
24
23
22 21 20 19
18
17 16 15 14
13 12
11 10
9
8
'/
6
b
4
3
2 1
24
22
21 20 19 18
17
16 15 14 13
12 11
10 9
8
7
6
b
4
3
2
1 23
A "AM
decimal position cannot be used.
1
255
LOGARITHM UNIT
1. The operating decimal point lies between columns 15 and 16. Plug the LIO-OUT.
BUSS
(24
20
r decimal point
15
10
5
O O O
5
LIO-OUT
24
21 20
15
10
Bottom Row
o c
10
!•<•••
9*s
5
(5) The determination of the characteristic of the logarithm is controlled by a pair of manually
set switches. These two dial switches, located to the right of the sequence mechanism, are
labeled "log N value". The switches must be set to the value 22 - n, where the operating deci-
mal point lies between columns n and n + 1 .
256
EXPONENTIAL UNIT
(1) The exponential unit requires:
•i • j__ J _ r i-U— L.,rcn i—J-^-s +Vi« T?T/~V (imintnr
pXUggmg l«J X'fcJelU. A ll'UUl 111C UU-OO im.u uic uiv «^v^«*»v^-
(2)
(3)
(4)
plugging to read the exponential function from the EIO counter into the buss,
plugging to terminate division; see Division.
At the start of the exponential computation, x stands with its decimal point at the operating
position. The EIO-IN must be plugged to read x from the buss into the EIO counter with deci-
mal point between columns 21 and 22.
The EIO-IN plughubs lie in row 27 and the corresponding buss plughubs in row 28 of the func-
tional plugboard.
Table 3 shows the necessary plugging of EIO-IN for each position of the operating decimal
point. The number at the top of each column refers to the buss plughub. The numbers in the
body of the table refer to the EIO-IN plughubs.
TABLE 3
EXPONENTIAL:
BUSS TO EIO-IN
BUSS COLUMNS
24 23
22
21 20 19 18
17
16
15
14
13
12
11
10
9 8
7
6
5
4 3
2 1
1/0
2/1
3/2
4/3
5/4
6/5
§ V*
33 8/7
| 9/8
ft 10/9
73 H/10
g 19/11
8 13/12
24
24
24
23
23 22
23 22
22 21
21 20
24
23
22 21
20 19
24
23
22
21 20
19 18
24
23
22
21
20 19
18 17
24
24
23
23 22
22
21
21
20
20
19
19 18
18 17
17 ID
16 15
24
23
22 21
20
19
18
17 16
15 14
24
24
23
OO
22
21
01 on
20 19
10
18
17
1 n
16
i« i*
15 14
id is
13 12
94
23
22
21
20
19 18
17
16
15
14 13
12 11
24
23
22
21
20
19
18 17
16
15
14
13 12
11 10
Q 14/13
g> 15/14
5 i 6 /i 5
g "/16
ft 18/17
24
23
22
21
20
19
18
17 16
15
14
13
12 11
10 9
24
23
22
21
20
19
18
17
16 15
14
13
12
11 10
9 8
24
23
22
21
20
19
18
17
16
15 14
13
12
11
10 9
8 7
24
23
22
21
2G
19
18
17
^ c
1 A 1 «J
i*± XO
1 o
11
i n
J.KJ
9 \j
7 6
24
23 22
21
20
19
18
17
16
15
14
13 12
11
10
9
8 7
6 5
° 19/18
24
23 22 21
20
19
18
17
16
15
14
13
12 11
10
9
8
7 6
5 4
on /1Q
OA
95 99 91 90
1Q
18
17
16
IS
14
13
12
11 10
9
8
7
6 5
4 3
21/20
22/21
24
24 23
23
22
22 21 20 19
21 2U iy its
18
17
17
ID
16
10
15
it
14
10
13
12
11
1U
10 9
V O
8
n
1
7
u
6
c
o
5 4
A O
-x o
3 2
o t
Ci i.
23/22
24 22
21
20 19 18 17
16
15
14
13
12
11
10
9
8 7
6
b
4
3 2
1 —
24/23
24 21
20
19 18 17 16
15
14
13
12
11
10
9
8
7 6
5
4
3
2 1
— ~ — —
1. The operating decimal point lies between columns 15 and 16. Plug the EIO-IN
r- decimal point
Row 27 o
Row 28
(24 21 20
0»00 000
15
10
m
o o o o o o EIO-IN
5
« — • • • • • BUSS
257
EXPONENTIAL UNIT
(5) At the end of the computation, the exponential function stands with its decimal point between
plughubs 21 and 22. The EIO-OUT must be plugged to read the exponential function into the
buss with decimal point at the operating position.
(6) The EIO-OUT plughubs lie in rows 30 and 31 and the corresponding buss plughubs in row 29 of
the functional plugboard.
(7) Table 4 shows the necessary plugging of EIO-OUT for each position of the operating decimal
point. The number at the top of each column refers to the buss plughub. The numbers in the
body of the table refer to the EIO-OUT plughubs.
F
rABLE 4
EXPONENTIAL:
EIO-OUT TO BUSS
BUSS COLUMNS
24 23
22
21
20
19
18
17 16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
1/0
— 44
43
42
41
40
39
38 37
36
35
34
33
32
31
30
29
28
27
26
25
24
23 22
2/1
— 43
42
41
40
39
38
37 36
35
34
33
32
31
30
29
28
27
26
25
24
23
22 21
3/2
— 42
41
40
39
38
37
36 35
34
33
32
31
30
29
28
27
26
25
24
23
22
21 20
4/3
— 41
40
39
38
37
36
35 34
33
32
31
30
29
28
27
26
25
24
23
22
21
20 19
5/4
— 40
39
38
37
36
35
34 33
32
31
30
29
28
27
26
25
24
23
22
21
20
19 18
6/5
— 39
38
37
36
35
34
33 32
31
30
29
28
27
26
25
24
23
22
21
20
19
18 17
§ V6
— 38
37
36
35
34
33
32 31
30
29
28
27
26
25
24
23
22
21
20
19
18
17 16
S3 8/7
— 37
36
35
34
33
32
31 30
29
28
27
26
25
24
23
22
21
20
19
18
17
16 15
§ 9/8
— 36
35
34
33
32
31
30 29
28
27
26
25
24
23
22
21
20
19
18
17
16
15 14
ft 10/9
-- 35
34
33
32
31
30
29 28
27
26
25
24
23
22
21
20
19
18
17
16
15
14 13
75 11/10
— 34
33
32
31
30
29
28 27
26
25
24
23
22
21
20
19
18
17
16
15
14
13 12
a 12/11
— 33
32
31
30
29
28
27 26
25
24
23
22
21
20
19
18
17
16
15
14
13
12 11
| 13/12
— 32
31
30
29
28
27
26 25
24
23
22
21
20
19
18
17
16
15
14
13
12
11 10
Q 14/13
-- 31
30
29
28
27
26
25 24
23
22
21
20
19
18
17
16
15
14
13
12
11
10 9
w> 15/14
— 30
29
28
27
26
25
24 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9 8
3 16/15
-- 29
28
27
26
25
24
23 22
21
20
19
18
17
16
15
14
13
12
11
10
9
8 7
u 17/16
- 28
27
26
25
24
23
22 21
20
19
18
17
16
15
14
13
12
11
10
9
8
7 6
a 18/17
° 19/18
— 27
26
25
24
23
22
21 20
19
18
17
16
15
14
13
12
11
10
9
8
7
6 5
-- 26
25
24
23
22
21
20 19
18
17
16
15
14
13
12
11
10
9
8
7
6
5 4
20/19
-- 25
24
23
22
21
20
19 18
17
16
15
14
13
12
11
10
9
8
7
6
5
4 3
21/20
-- 24
23
22
21
20
19
18 17
16
15
14
13
12
11
10
9
8
7
6
5
4
3 2
22/21
— 23
22
21
20
19
18
17 16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
23/22
- 22
21
20
19
18
17
16 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1 --
24/23
— 21
20
19
18
17
16
15 14
13
12
11
10
9
8
7
6
5
4
3
2
1
2. The operating decimal point lies between columns 15 and 16. Plug the EIO-OUT.
BUSS
Row 29 oo
24
Row 30
20 15
r- decimal point
10
£
25
21 20
15
10
o o o o o o
5
EIO-OUT
Row 31 ooooo ooooo ooooo ooooo o • 9 1 • % EIO-OUT
45 40 35 30
258
X M.1K* OiXXt
,rl 1 /9t
SINE UNIT
klfJTTO i«^r* ¥\>£
B. read x/27r from the buss into the SIO counter,
C. read the decimal part of x/2ir from the SIO counter into the buss,
D. read sin x from the SIO counter into the buss,
E. multiply at the operating decimal position; see Multiplication.
(2) In the table relays, l/2?r stands with its decimal point between columns 22 and 23. The read-
out of the table relays must be plugged to read 1/277 into the buss with decimal point at the
operating position.
(3) The 1/27T plughubs lie in row 20 and the corresponding buss plughubs in row 19 of the MP-DIV
plugboard.
(4) Table 5 shows the necessary plugging of the read-out of l/2ir for each position of the operating
decimal point. The number at the top of each column refers to the buss piughub. The numbers
in the body of the table refer to the l/2ir plughubs.
BUSS COLUMNS
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
987 6 5432
1/0
2/1
3/2
4/3
5/4
This decimal position cannot be used.
22
22
22 21
22 21 20
21 20 19
6/5
22
21
20
19 18
§ V6
22
21
20
19
18 17
33 8/7
22
21
20
19
18
17 16
g 9/8
22
21
20
19
18
17
16 15
ft 10/9
22
21
20
19
18
17
16
15 14
75 ii/io
22 21
20
19
18
17
16
15
14 13
S 12/11
22
21 20
19
18
17
16
15
14
13 12
g 13/12
22
21
20 19
18
17
16
15
14
13
12 11
Q 14/13
22
21
20
19 18
17
16
15
14
13
12
11 10
g> 15/14
22 21
20
19
18 17
16
15
14
13
12
11
10 9
a l6 / 15
22 21 20
19
18
17 16
15
14
13
12
11
10
9 8
S 17 /16
22 21 20 19
18
17
16 15
14
13
12
11
10
9
8 7
a 18/17
22 21 20 19 18
17
16
15 14
13
12
11
10
9
8
7 6
~ iy/ib
22 21 20 19 18 17
16
15
14 13
12
11
10
9
8
7
6 5
20/19
22 21 20 19 18 17 16
15
14
13 12
11
10
9
8
7
6
5 4
21/20
22 21 20 19 18 17 16 15
14
13
12 11
10
9
8
7
6
5
4 3
22/21
22 21 20 19 18 17 16 15 14
13
12
11 10
9
8
7
6
5
4
3 2
23/22
22 21 20 19 18 17 16 15 14 13
12
11
10 9
8
7
6
5
4
3
2 1
24/23
Use this decimal position with caution.
1. The operating decimal point lies between columns 15 and 16. Plug the read-out of 1/27T.
Row 19 ooooo ooooo
24 20
BUSS
15
10
r- decimal ooint
Row 20 o o o »-h
24 22
20
15
10
oo ooooo 1/2 ir
5
259
SINE UNIT
(5) In the buss, x/2ir stands with its decimal point at the operating position. The SIO-IN II must be
plugged to read x/27T into the SIO counter at the same decimal position; i.e., the plugging is
direct.
(6) The SIO-IN n plughubs lie in row 32 and the corresponding buss plughubs in row 33 of the
functional plugboard.
2. Plug SIO-IN II
Row 32 o
Row 33
SIO-IN n
BUSS
(7) In the SIO counter, x/2;r stands with its decimal point at the operating position. The SIO-OUT I
must be plugged to read x/2n into the buss with its decimal point between columns 22 and 23.
(8) The SIO-OUT I plughubs lie in row 35 and the corresponding buss plughubs in row 34 of the
functional plugboard.
(9) Table 6 shows the necessary plugging of SIO-OUT I for each position of the operating decimal
point. The number at the top of each column refers to the buss plughub. The numbers in the
body of the table refer to the SIO-OUT I plughubs.
TABLE 6 SINE: SIO-OUT I TO BUSS
BUSS COLUMNS
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
1/0
2/1
3/2
4/3
5/4
6/5
§ V6
3 8/7
| 9/8
P< 10/9
13 H/10
5 12/11
g 13/12
Q 14/13
g> 15/14
| 16/15
6 1V16
§ 18/17
° 19/18
20/19
21/20
22/21
23/22
24/23
1
2
3
4
5
6
7
8
9
10
This decimal position cannot be used.
11 10
12 11
1
2
3
4
5
6
7
8
9
10
13 12 11
14 13 12
15 14 13
16 15 14
17 16 15
18 17 16
19 18 17
20 19 18
21 20 19
22 21 20
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
11 10 9
12 11 10
1
2
3
4
5
6
7
8
13 12 11 10 9
14 13 12 11 10
1
2
3
4
5
6
7
8
15 14 13 12 11 10 9
16 15 14 13 12 11 10
1
2
3
4
5
6
7
8
17 16 15 14 13 12 11 10 9
18 17 16 15 14 13 12 11 10
1
2
3
4
5
6
7
8
19 18 17 16 15 14 13 12 11 10 9
Use this decimal position with caution.
260
PLUGGING INSTRUCTIONS
1 UK UJJCl itllllg UCVillliaJ. ^IWiiiu lieu ucmccii i,uiuiimt) .•. «/ auu j.v. a »"6 w»*%*-**w> * » ■
decimal point
Row 34 ooo
24 22 20
15
10
oo ooooo BUSS
5
Row 35 ooooo ooooo • • • • • • > • i • 1 • • • • SIO-OUT I
24 20 15 10 5
(10) At the end of the computation, sin x stands in the SIO counter with decimal point between col-
ums 22 and 23. The SIO-OUT II must be plugged to read the sine into the buss with decimal
point at the operating position.
(11) The SIO-OUT II plughubs lie in row 36 and the corresponding buss plughubs in row 37 of the
functional plugboard. The auxiliary nines, necessary if the sine is negative, lie in the ten plug-
hubs of the left side of the bottom row of the same board. Since only ten such auxiliary nines
are available, special provisions must be made for computing the sines of third and fourth
quadrant angles if there are eleven or fewer operating decimal places. See Coding. Sine Unit.
(12) Table 7 shows the necessary plugging of SIO-OUT II for each position of the operating decimal
point. The number at the top of each column refers to the buss plughub. The numbers in the
body of the table refer to the SIO-OUT II plughubs, except that "9' s" refers to any of the ten
plughubs at the right side of the bottom row of the functional plugboard.
TABLE 7 SINE: SIO-OUT H TO BUSS
BUSS COLUMNS
24
23
22 21
20
19 18 17 16 15 14 13 12 11
10 9
8
7
6
5
4
3
2 1
1/0
This decimal position cannot be used.
2/1
24
23 22
3/2
24
23
22 21
4/3
24
Ark
43
22
21 20
5/4
24
23
22
21
20 19
6/5
24
23
22
21
20
19 18
§ 7/6
24
23
22
21
20
19
18 17
5 8/7
24
23
22
21
20
19
18
17 16
§ 9/8
24
23
22
21
20
19
18
17
16 15
ft 10/9
24
23 22
21
20
19
18
17
16
15 14
■a n/io
24
23
22 21
20
19
18
1 »7
16
15
14 13
.5 12/11
24
Z6 ZZ
Ai ZU
iy
i«
17
10
10
14
13 12!
8 13/12
24
9te
9fe 9fe
9te
9te 9te 9's 9's 9's 9te 23 22 21
20 19
18
17
16
15
14
13
12 11
Q 14/13
24
9te
9's 9's
9te
9's 9's 9te 9!s 9fe 23 22 21 20
19 18
17
16
15
14
13
12
11 10
g 5 15/14
24
9fe
9te 9fe
9te
9's 9te 9's 9fe 23 22 21 20 19
18 17
16
15
14
13
12
11
10 9
3 16/15
24
9's
9's 9te
9te
9's 9te 9te 23 22 21 20 19 18
17 16
15
14
13
12
11
10
9 8
S 1V16
24
9's
9's 9's
9fe
9's 9's 23 22 21 20 19 18 17
16 15
14
13
12
11
10
9
8 7
§ 18/17
w 19/18
24
9%
9's 9te
9fe
9te 23 22 21 20 19 18 17 16
15 14
13
12
11
10
9
8
7 6
24
9te
9's 91s
9fe
23 22 21 20 19 18 17 16 15
14 13
12
11
10
9
8
7
6 5
20/19
24
9's
9te 9te
23
22 21 20 19 18 17 16 15 14
13 12
11
10
9
8
7
6
5 4
21/20
24
9's
9's 23
22
21 20 19 18 17 16 15 14 13
12 11
10
9
8
7
6
5
4 3
22/21
24
9te
23 22
21
20 19 18 17 16 15 14 13 12
11 10
9
8
7
6
5
4
3 2
23/22
24
23
22 21
20
19 18 17 16 15 14 13 12 11
10 9
8
7
6
5
4
3
2 1
24/23
Use this decimal position with caution.
261
SINE UNIT
4. The operating decimal point lies between columns 15 and 16. Plug SIO-OUT II .
decimal point
Row 36 o •
24 22 20
Row 37 o
15
10
oo o o o o o SIO-OUT II
5
24
Bottom
Row
20 15
-•— •
BUSS
10
262
INTERPOLATORS
(1) The plugging of each interpolator unit is complete ana independent i. A - u e, _o ^^ - -*
polator unit, the following quantities must be specified:
A. the interval of the argument or the highest order "h",
B. the tape decimal point,
S; £ Z£ 3 StStiJ^oelicients (induding C ) accompanying each argument,
E. the operating decimal point.
(2) An interpolator unit requires:
A plugging to read the argument from the buss into the interpolation counter,
b' plugging to read "h correction- 2" into the intermediate counter,
n r>it,o-<rin«r tn r* a d "h correction- 3" into the intermediate counter,
d' Dlueeine to read "h" from the buss into the intermediate counter,
E plulginltoread the interpolation^ coefficients from the buss to the intermediate counter,
F. a switch setting of ^^^^^ a »^^^*te^ludii« Cn) accompany-
U. a swucn seuingui cue uumuw <-«. un.en- Ui ^ * > «
ing each argument,
H. plugging to multiply at the operating decimal position; see Multiplication.
(3)
In order to position a functional tape to the nearest value of the argument, six columns of the
buss must be plugged to the interpolation counter. These six columns include the algebraic
sLnc^mn the four argument columns and the highest order 'V column. In order to position
XctS'tape to the next lower value of the argument, only five columns of the buss are
Plugged to the interpolation counter. The plugging from the highest order "h" column to the
first column of the interpolation counter is omitted.
(4) The interpolation counter plughubs and the corresponding buss plughubs lie in the following rows:
Interpolator I -functional plugboard, row 15 INTERPOLATION-IN-1, row 16 BUSS;
Interpolator II - MP-DIV plugboard, row 12 I-IN-1-2 row 11 BUSS;
Interpolator m - MP-DW plugboard, row 13 I-IN-1-3, row 14 BUSS.
(5)
Table 8 shows the necessary plugging for the read-in of the argument to the interpolation counter
for each highest order "h" column. The number at the top of each column refers to the inter-
polation counter plughub. The numbers in the body of the table refer to the buss plughubs.
i mu~ «„«»„««„ Aonirr,<>\ r,nint lips h^twppn columns 15 and 16. Plug the interpolation count-
er for the following values of Aa and highest order h .
Interpolator
II
m
Aa
0.1
0.01
0.001
Highest Order "h r
14
13
12
INTERPOLATORS
263
FUNCTIONAL PLUGBOARD
Row 15
Row 16
o » •— »
6 5 4 3
• • • 000 ooooo 00000
3\ 2 1
ooooo I-IN-1
o • oo o
24
MP-DIV PLUGBOARD
Row 11
o^o o o
24
Row 12
Row 13
o o
20
•— •■
20
15
ooooo
10
ooooo
5
oS
• 94 •— •
6 5 4 3 2 1
7i • • 00 ooooo ooooo
15 10 5
000 ooooo ooooo ooooo
Row
is o • • • • — •— • 000 ooooo ooooo ooooo
[6543X21
14 0»000 0000 • — • • • • o ooooo ooooo
BUSS
BUSS
I-IN-1-2
I-IN-1 -3
BUSS
24
20
15
10
(6) If h is negative, the "h" correction- 2 reads auxiliary nines into the columns of the intermediate
counter to the left of the highest order "h" column. If it is desired to read these auxiliary
nines into a storage counter A under control of the line of coding (841, A, blank), the "h" cor-
rection^ plughubs should be plugged to any available row of buss plughubs instead of to the
intermediate plughubs.
TABLE 8
INTERPOLATION: BUSS TO INTERPOLATION COUNTER
INTERPOLATION COUNTER COLUMNS
6 5 4 3 2 1
1
24 5 4 3 2 1
2
24 6 5 4 3 2
3
24 7 6 5 4 3
4
24 8 7 6 5 4
5
24 9 8 7 6 5
5 6
24 10 9 8 7 6
3 7
24 11 10 9 8 7
o 8
24 12 11 10 9 8
° 9
24 13 12 11 10 9
jh 10
24 14 13 12 11 10
1 11
24 15 14 13 12 11
•g 12
24 16 15 14 13 12
gis
Z> 14
24 17 16 15 14 13
24 18 17 16 15 14
3 15
24 19 18 17 16 15
■a i6
24 20 19 18 17 16
3 17
24 21 20 19 18 17
18
24 22 21 20 19 18
19
24 23 22 21 20 19
20
24 — 23 22 21 20
21
24 — — 23 22 21
22
24 - 23 22
264
PLUGGING INSTRUCTIONS
.... _ . , , j jli__ — ^ji«o, t«ioi.maHiqfa nniiritpr nlughubs lie in the
(7) The "h" correction-2 piugnuDs ana me cuneDyvuuxiiB i«i. C imv».d < r — &*-
following rows:
interpolator I - functional plugboard, row 19 H-CORR-2, row 20 INTERMED-IN-2;
Interpolator n - MP-DIV plugboard, row 21 H-CORR-2-2 row 22 INT;
Interpolator in - MP-DIV plugboard, row 25 H-CORR-3-2, row 26 INT.
(8) Table 9 shows the necessary plugging for reading the "h" correcti on-2 ^^J^l^nml
W intermediate counter for each highest order "h" column The number at the op of each ^column
refers to the intermediate plughub. The numbers in the body of the table refer to the h cor-
rection plughubs.
TABLE 9 INTERPOLATION: -n" ^umvr.^iiwn-* iv^^xviv.—
COUNTER
INTERMEDIATE COUNTER COLUMNS
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
7
b
5 4 3 2
1
1
24 23 22 21 20 19 18 17 16 15 14 13 12 11- 10 9
8
7
6
5 4 3 2
?,
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
7
b
5 4 3
3
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
7
b
5 4
4
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
7
b
5
R
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
7
b
C
fi
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
i
s
7
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
8
1— 1
o
8
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
u
9
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
j3
10
24 23 22 21 20 19 18 17 16 15 14 13 12 11
11
24 23 22 21 20 19 18 17 16 15 14 13 12
I O
12
24 23 22 2i 20 19 16 17 16 15 14 13
T3
13
24 23 22 21 20 19 18 17 16 15 14
1 o
14
24 23 22 21 20 19 18 17 16 15
02
CD
15
24 23 22 21 20 19 18 17 16
b0
16
24 23 22 21 20 19 18 17
•rH
17
18
19
20
21
22
24 23 22 21 20 19 18
24 23 22 21 20 19
24 23 22 21 20
24 23 22 21
24 23 22
| 24 23
2. The operating decimal point lies between columns 1 5 and 16. Plug "h" correction-2 for the
following values of Aa and highest order "h".
Interpolator
Aa
Highest Order "h"
I
0.1
14
II
0.01
13
III
0.001
12
INTERPOLATORS
265
FUNCTIONAL PLUGBOARD
Row 19 o • • • • — i
24
20
Row 20 o
24
20
-•oooo ooooo ooooo H-CORR-2
15 10 5
-•oooo ooooo ooooo INT-IN-2
15 10 5
MP-DIV PLUGBOARD
Row 21 o » • • •
24
Row 22 o
24
20
20
-•— • ooo oo'ooo ooooo H-CORR
15 10 5 -2-2
■♦— • ooo ooooo ooooo INT
15 10 5
Row 25 o
Row 26 o
24
24
20
20
15
15
oo ooooo ooooo H-CORR
10 5 -3-2
oo ooooo ooooo INT
10 5
(9) In order to read minus one to lowest order "a" column, columns 1-23 of the "h" correction- 3
plughubs provide nines and the 25th plughub provides an eight. The "8" plughub is connected to
the lowest order "a" column of the intermediate counter. The nine plughubs are connected to
the remaining 23 columns of the intermediate counter. If it is desired to read the minus one of
"h" correction-3 into a storage counter A under control of the line of coding (841, A, blank),
the "h" correction-3 plughubs should be plugged to any available row of buss plughubs instead
of to the intermediate plughubs.
(10) The intermediate counter plughubs and the corresponding "h" correction-3 plughubs lie in the
following rows:
Interpolator I - functional plugboard, row 21 INTERMED-IN-2, row 22 H-CORR-3;
Interpolator II - MP-DIV plugboard, row 23 INT, row 24 H-CORR- 2- 3;
Interpolator in - MP-DIV plugboard, row 27 INT, row 28 H-CORR- 3- 3.
(11) Table 10 shows the necessary plugging for reading "h" correction-3; i.e., minus one, to the
intermediate counter for each highest order "h" column. The number at the top of each column
refers to the intermediate counter plughub. The numbers in the body of the table refer to the
"h" correction-3 plughubs, except that ' 8' refers to the 25th plughub of the "h" correction-3 row.
3. The operating decimal point lies between columns 15 and 16. Plug "h" correction-3 for the
following values of Aa and highest order "h".
Interpolator
Aa
Highest Order "h"
I
0.1
14
II
0.01
13
HI
0.001
12
266
PLUGGING INSTRUCTIONS
FUNCTIONAL PLUGBOARD
Row 21
Row 22
MP-DIV PLUGBOARD
Row 23
Row 24
Row 27
INT-IN-2
H-CORR-3
Row 28 •-•
INT
H-CORR
-2-3
INT
H-CORR
-3-3
TABLE 10 INTERPOLATION: "h" CORRECTION- 3 TO INTERMEDIATE COUNTER
INTERMEDIATE COUNTER COLUMNS
h-
1
2 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
'8' 1
2
3 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
'8 1
2 1
3
4 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
'8'
3
2 1
4
5 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
'8'
4
3
2 1
5
6 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
'8'
5
4
3
2 1
S
3
6
7 23
22
21
20
IS
18
ii
16
15
•i A
11
13
t n
14
11
10
9
8
Inl
O
o
5
A
*x
3
ft ■*
7
8 23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
•8'
7
6
5
4
3
2 1
O
8
9 23
22
21
20
19
18
17
16
15
14
13
12
11
10
'8'
8
7
6
5
4
3
2 1
O
9
10 23
22
21
20
19
18
17
16
15
14
13
12
11
'8 1
9
8
7
6
5
4
3
2 1
J5
10
11 23
22
21
20
19
18
17
16
15
14
13
12
■8'
10
9
8
7
6
5
4
3
2 1
?H
ii
12 23
22
21
20
IS
18
17
16
15
14
13
In 1
O
11
10
9
8
7
6
5
4
3
2 1
12
13 23
22
21
20
19
18
17
16
15
14
'8'
12
11
10
9
8
7
6
5
4
3
2 1
u
n
13
14 23
22
21
20
19
18
17
16
15
'8'
13
12
11
10
9
8
7
6
5
4
3
2 1
-M
14
15 23
22
21
20
19
18
17
16
•8'
14
13
12
11
10
9
8
7
6
5
4
3
2 1
CD
15
16 23
22
21
20
19
18
17
'8'
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
be
16
17 23
22
21
20
19
18
'8'
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
Hi
17
18 23
22
21
20
19
'8'
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
18
19 23
22
21
20
'8'
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
19
20 23
22
21
'8 1
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
20
21 23
22
•8 1 -
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
21
22 23
; 8'
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
22
23 '8'
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2 1
267
INTERPOLATORS
(12) The "h" columns must be plugged to read from the buss into the intermediate counter; i.e., the
highest order "h" column and the columns to its right are plugged. Since the multiplications
necessary to interpolation are carried on at the operating decimal position, this plugging is
direct.
(1 3) The intermediate counter plughubs and the corresponding buss plughubs lie in the following rows:
Interpolator I - functional plugboard, row 23 INTERMED-IN-2, row 24 BUSS;
Interpolator H - MP-DIV plugboard, row 16 INT-IN-3, row 15 BUSS;
Interpolator IH - MP-DIV plugboard, row 17 INT-IN-4, row 18 BUSS.
(14) Table 11 shows the necessary plugging for the read-in of "h" from the buss to the intermediate
counter for each highest order "h" column. The number at the top of each column refers to the
buss plughub. The numbers in the body of the table refer to the intermediate counter plughubs.
TABLE 11 INTERPOLATION: BUSS TO INTERMEDIATE -
IN-2
> 3,
OR 4
BUSS COLUMNS
24 23 22 21 20 19 18
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
1
2
2 1
3
3
2 1
4
4
3
2 1
5
5
4
3
2 1
B
3
6
6
5
4
3
2 1
7
7
6
5
4
3
2 1
O
8
8
7
6
5
4
3
2 1
o
9
9
8
7
6
5
4
3
2 1
A
10
10
9
8
7
6
5
4
3
2 1
U
11
11 10
9
8
7
6
5
4
3
2 1
0)
12
12 11 10
9
8
7
6
5
4
3
2 1
u
o
13
13 12 11 10
9
8
7
6
5
4
3
2 1
-M
14
14 13 12 11 10
9
8
7
6
5
4
3
2 1
15
15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
16
16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
n
17
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
18
18
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
19
19 18
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
20
20 19 18
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
21
21 20 19 18
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
22
22 21 20 19 18
17 16 15 14 13 12 11 10
9
8
7
6
5
4
3
2 1
4. The operating decimal point lies between columns 15 and 16. Plug the read- in of "h" for
the following values of Aa and highest order "h".
Interpolator
Aa
Highest Order "h"
I
0.1
14
n
0.01
13
m
0.001
12
268
PLUGGING INSTRUCTIONS
Row 23 ooooo ooooo o
24 20 15
10
Row 24
o o o oo
24
MP-DIV PLUGBOARD
Row 15
Row 16
ROW I?
Row 18
ooooo
24
ooooo
24
ooooo
24
ooooo
24
ooooo
20
ooooo
20
ooooo
20
ooooo
20
o (
15
o o
15
o o
15
-•-• INT-IN-2
10
BUSS
BUSS
10
10
o o o •-
15
10
ooooo ooo
20 15
INT-IN-4
BUSS
10
(1 5^ The interoolator units read the interpolational coefficients from the functional tape into the
buss with decimal point at the tape decimal position. The coefficients must be read from the
buss into the intermediate counter (C-value plughubs) for computation at the operating decimal
position, Negative coefficients may not be shifted to the right, since no auxiliary nines are
available to fill in at the left.
(16) The intermediate counter (C-value) plughubs and the corresponding buss plughubs lie in the
following rows of the MP-DIV plugboard:
Interpolator I, row 5 C-VALUE-1, row 6 BUSS;
Interpolator II, row 8 C-VALUE-2, row 7 BUSS;
Interpolator in, row 9 C-VALUE-3, row 10 BUSS.
5. The operating decimal point lies between columns 15 and 16. Plug interpolators I and III
for tape decimal point between columns 15 £ ' '" ~
point between columns 9 and 10, JC k J < 10*
MP-DIV PLUGBOARD
for tape decimal point between columns 15 and 16. Plug interpolator II for tape decimal
Row 5 o
Row 6 o
Row 7 o
Row 8 o ^
24
24
20
15
10
5
24
20
15
10
5
f24
20
15
10
5
1
C-VAL-1
BUSS
BUSS
C-VAL-2
20
15
10
269
INTERPOLATORS
MP-DIV PLUGBOARD
Row 9 o • • • •
24
20
15
Row 10 o
10
C-VAL-3
BUSS
24
20
15
10
6. The operating decimal point lies between columns 15 and 16. In the functional tape, Aa = 0.1
and highest order "h" = 14. The tape decimal point lies between columns 15 and 16. Plug
interpolator I.
FUNCTIONAL PLUGBOARD
Row 15 o • • • • — •— • ooo ooooo ooooo ooooo I-IN-1
[654 3\2 1
o • o o o oo • • » • • ooo ooooo oooo
Row 16
24 20
Rows 17 and 18 not used.
o BUSS
15
10
Row 19 o
Row 20 o
24
24
Row 21
Row 22
o • «
[24
o i
24
20
20
20
20
-•oooo ooooo ooooo H-CORR-2
15 10 5
-•oooo ooooo ooooo INT-IN-2
15 10 5
1 ,
15
l*
10
10
INT-IN-2
H-CORR-3
Row 23 ooooo ooooo oi
24 20 15
Row 24 ooooo ooooo o<
24 20 15
10
10
INT-IN-2
BUSS
MP-DIV PLUGBOARD
Row 5 o • • • •
24
20
15
Row 6 o
24
20
15
10
10
C-VAL-1
BUSS
7 . The operating decimal point lies between columns 1 5 and 16. In the functional tape , Aa = .01 ,
highest order "h" = 13 and|C k | < 10 9 . The tape decimal point lies between columns 9 and
10. Plug interpolator n.
270
PLUGGING INSTRUCTIONS
MP-uIV PLUGBOARD
Row 7 o
Row 8
o • i
[24
o » i
20
15
10
BUSS
C-VAL-2
24 20 15
Row 11 o • o o o 000 •— *
10 5
oo ooooo ooooo BUSS
Row 12
O • O O O 000 •— • — • • • 00 OOOOO uuuuu xjuwjkj
p4 20 /15 10 5
o \ i t 1 »— « 000 ooooo ooooo ooooo I-IN-1-2
6 5 4 3 2 1
Row 15 ooooo ooooo oo
ftA on K
Row 16 OOOOO OOOOO 00
24 20 15
m
BUSS
INT-IN-3
Row 21 o
Row 22 o
24
20
9 9 • • • • • • • • • • •
10 5
ooo ooooo ooooo H-CORR
15 10 5 -2-2
-•— • ooo ooooo ooooo INT
24
20
Row 23
Row 24
o • -
[24
ft I
20
15
71
15
10
10
1° *
1 24
20
15
10
INT
H-CORR
-2-3
8. The operating decimal point lies between columns 15andl6. In the functional tape, Aa = 0.001
and highest order "h" = 12. The tape decimal point lies between columns 15 and 16. Plug
interpolator III.
MP-DIV PLUGBOARD
Row 9 o • • • • — • • • • * — • • •
24
20
15
now iu u
24
20
• • 9
-6 — • — • • — • — • — •— • C-VAL-3
10
RTISS
ROW 13 Op •-*
ROW 14 O
15 10 5
«— • ooo ooooo ooooo ooooo I-IN-1-3
• % — % m — • ooo uuuuu uuuu
p 5 4 3\2 1
>ooo oooo • — • m • • o o o o o
9.a 20 15 10
Row 17 ooooo ooooo ooo
24 20 15
Row 18 ooooo ooooo ooo
24 20 15
o ooooo BUSS
5
10
INT-IN-4
BUSS
10
INTERPOLATORS
271
MP-DIV PLUGBOARD
Row 25 o • • • »
24
20
Row 26 o
24
20
Row 27
Row 28
15
15
o
8
J 24
20
15
10
5
24
20
15
10
5
oo ooooo ooooo H-CORR
10 5 -3-2
oo ooooo ooooo INT
10 5
INT
H-CORR
-3-3
(17) For tape positioning, one half the number of arguments in the tape must be set in the push
button switches labeled "Value tape set up 1/2 A values in tape" above the interpolator to be
employed.
(1 8) The number of interpolational coefficients (including C Q ) should be set in each of the dial switches
above the interpolator, labeled "Set up number of C-values on each switch". In certain special
cases, the dial switches need not be set alike. In order to position the tape, the right dial switch
is set to the number of interpolational coefficients (including Cq) accompanying each argument
in the tape. The left dial switch is set to the number of interpolational coefficients to be used
in the interpolation computation.
272
CARD FEEDS
/1\ t<v.« now* faaAc ronniro nlucrorintr fnt« the r^ad-nut from the card feed brushes into the buss.
The card columns and corres^ondin 0, card feed brushes and plughubs are numbered from left to
right, whereas the buss plughubs or the calculator are numbered from right to left.
(2) If negative numbers are to be shifted to the left on reading into the calculator, they should be
punched as complements on ten rather than on nine. If negative numbers are to be shifted to
the right on reading into the calculator, auxiliary nines must be filled in to the left by plugging
one brush plughub to more than one buss plughub. One brush plughub should not be plugged to
more than nine buss plughubs.
(3) The card feed plugboard is located to the right of the sequence mechanism. The brush plughubs
of card feed I lie in vertical row 8 and the corresponding buss plughubs in vertical row 5. The
brush plughubs of card feed II lie in vertical row 4 and the corresponding buss plughubs in ver-
tical row 1 .
1. The operating decimal point lies between columns 15 and 16. Cards are to be fed from
both feeds with decimal point between card columns 9 and 10. Plug the card feeds.
CARD CARD
BUSS FEED BUSS FEED
II I
24 • o o 1* 24 • o o 1*
too iioo *
too f f o o
too 4 i o o
o o 5* 204 o o
10 o • 4 o o
o o 4 * o o
O 6^00
O O • • o o
o o 104| 15^ o o
V
1 • o O I
oo 1 4 o o i
• • o I
o o I if o o i
o o 15f 10* o o 15<
oo 4*00
o o i * o o
o o 20 i 5« o o <
oo ••oo
o o ••oo
oo ••oo
o o 24 4 ll o o 24 1
The operating decimal point lies between columns 15 and 16. Cards are to be fed from
feed I with decimal point between card columns 15 and 16. Cards are to be fed from feed
II with decimal point between card columns 3 and 4.
273
CARD FEEDS
CARD
CARD
BUSS
FEED BUSS
FEED
II
I
24
>
% 24.
1
»
»
lo
o
»
20
»
5.
► 20i
»
5o
»
>
>
>
»
o
»
15(
I
I
>
10<
► 15<
I
10<
»
>
>
► o
I
►
>
►
10(
>
*
15i
► 10(
: :
►
►
y o
o
15<
> o
►
J
»
o c
5<
►
20 o 5 c
o
20 1
>
o o
► o
o o
o
o
o o
lJ
24 o
lo
24 <
(4) The "Card Feed Reverse" switches are located to the left of the sequence mechanism. It should
be noted that though these switches reverse the codes of the feeds they do not reverse the plug-
ging.
274
CARD PUNCH
/i\ rri,„ „„wi ™™^ romiiras nhio-ffintr nf the read-in from the Dunch counter to the punch magnets.
The card columns are numbered from left to right, whereas the punch counter columns are
numbered from right to left.
(2) To skip a card out, 24 card columns must be punched. If fewer than 24 columns are wired for
punching, zeros in a master card in the duplicating rack will skip the card out.
(3) The plugboard for the card punch is located at the extreme right end of the machine, inside the
cover. Only two sets of plughubs are used, labeled PUNCH MAGNETS and COMP MAG OR
CTR TOT EXIT OR M S IN, the latter set being wired to the punch counter.
1 . The operating decimal point lies between columns 15 and 16. Plug the punch to punch cards
with decimal point between columns 9 and 10.
PUNCH MAGNETS
Card cols. 1-20
Card cols. 21-24
Ctr. cols. 24- 5
Ctr. cols. 4-1
! 25
t iU i o
oooooo ooooo 00000
COMP MAG OR CTR TOT EXIT OR M S IN
2A 2B 4A 4B 6A
6B
6B
• li 9 9
oooooooo 00000000
(4) Cards may be punched containing a function in the first columns of the cards and a serial num-
ber in the last columns of the card. After the function is punched, a duplicating card and skip
bar control the punch.
2. The operating decimal point lies between columns 15 and 16. A function is to be punched
in the first 24 card columns with decimal point between card columns 9 and 10. Serial
numbers are to be punched in card columns 70, 73-76 and 79. Plug the punch.
/
/
o o
o o
2A
V*U
PUNCH MAGNETS
5 10 15 20
-#— • — *7 — m » 9 — » t •
7\
^-# • » • — •■
25
30
n n n r\ r» n n n
2B
4t) DU
0000 oooo
65 \^>^~
• • ^-«
COMP MAG OR CTR
4A 4B
35
n n r» o
00
OOOO
75
TOT EXIT OR
6A
40
o o
o o
^
ou
o o
80
MS IN
6B/
\6B 1
#»-• •• 0000 0000 0000 0000
275
PRINTING
(1) The printing operation requires plugging for:
A. dropping off zeros to the left,
B. printing a minus sign,
C. the read-out of the print counter to the typewriter,
D. horizontal spacing of digits,
E. printing a decimal point,
F. dropping off zeros to the right,
G. tabulating and returning the carriage,
H. resetting print and print step counters,
I. vertical spacing,
J. adding a half -correction,
K. printing in half time.
(2) The plugging of each typewriter is complete and independent. The sequence of printing oper-
ations is controlled by a print step counter which advances at the rate of nine steps per second.
The read-out of this counter is wired to 49 column selection plughubs, labeled COL-SEL-PRINT-1
and lying in rows 1,2 and 3 of the functional plugboard for typewriter I, and COL -SEL -PRINT -2
lying in rows 8, 9 and 10 of the functional plugboard for typewriter II.
(3) In order to drop off zeros to the left, for typewriter I:
A. plughubs 24 and 25 of row 5 (RO-CONTROL-RELS) are connected,
B. plughub 25 of row 6 is plugged to the n + 2nd plughub of row 5, where the printed deci-
mal point lies between columns n and n + 1 of the print counter.
In order to drop off zeros to the left, for typewriter II:
A. plughubs 24 and 25 of row 12 (RO-CONTROL-RELS) are connected,
B. plughub 25 of row 13 is plugged to the n + 2nd plughub of row 12, where the printed
decimal point lies between columns n and n + 1 of the print counter.
No plughubs are available for dropping off zeros to the left if the printed decimal point lies
between columns 22 and 23 or between columns 23 and 24. If for typewriter I the 25th plughub
of row 6 is plugged to the 23rd plughub of row 5, or if for typewriter II the 25th plughub of row
13 is plugged to the 23rd plughub of row 12, then,
(a) if the printed decimal point lies between columns 22 and 23, decimal quantities will be
printed with no zero preceding the decimal point;
(b) if the printed decimal point lies between columns 23 and 24, decimal quantities will be
printed with no zero preceding the decimal point and if the digit following the decimal
point should be a zero, a space will occur instead of a printed zero.
(4) In order to print the minus sign preceding a negative number, the plughub of the print counter
read-out next above the plughub wired to print the highest significant digit must be plugged to a
column selection plughub. Negative numbers may be printed as complements on nine by throw-
ing the "Print Complement Switches" located to the right of the MP-DIV plugboard.
(5) The plughubs of the print counter read-out corresponding to the columns of the print counter
containing the digits to be printed must be plugged to column selection plughubs. The print
counter read-out plughubs are in row 4 for typewriter I and row 11 for typewriter II.
(6) If the digits of the quantity to be printed are to be spaced in horizontal groups, spaces must be
plugged from plughubs 11-25 of row 3 for typewriter I, from plughubs 11-25 of row 10 for type-
writer n. These spaces are plugged to the appropriate column selection plughubs between the
connections from the print counter read-out plughubs.
276
PLUGGING INSTRUCTIONS
K')
(8)
(9)
/i,q\
mK- ->-.-* -rt^l ^. — '— ^ -- — 1 — rrrm'l *•*--» — il-- OCJ-l. ~1~~U..U n( «.«-vrt 1 fnii ^nrifiTgrnitaK T Itf Wrtin ft fr»l* hmfl.
ifle utjCiHlai puuiL us uxuggSu Iruiu uic aot.11 piugiiuD <-»a iuii ■»■ Ivjx ijyeAiivei ■*•» oi **"» « i% '* vr-
. u. tt ±~ 4.1 _„i..— ~_ „„!_,, 4-: ~— .l„»i«,k I'ttSm/v Un4-nrnAn 4-Vi«->0f> turn nlnrrhiiKc whinVi oro ynnnoptpd
WXltei. ii, lu uic t;uiuuui scickuuu (;iuguuu j.jrxiig ucuntcu iuvscje >.t»w ^.iv^m..^ mi****. •*..» „ «~—
to the print counter read-out columns either side of the assumed decimal point.
Zeros may be dropped off to the right of a quantity under control of the code 87 (called the
"argument control") in the Out column of the line of coding initiating printing. One of the first
two plughubs in row 18 is connected to the column selection plughub next after the plughub con-
nected to the last digit to be printed.
If only one vertical column of numbers is to be printed, a tab is plugged immediately after the
last digit, five column selection plughubs are left blank and a second tab is plugged for the car-
riage return. This second tab iF converted to a carriage return by adjusting the right hand
margin stop. If more than one vertical column of numbers is to be printed, a tab is plugged
immediately after the last digit of each quantity. The tab after the last quantity printed on any
horizontal line is converted to a carriage return. Eight tab plughubs are provided for each
typewriter. They are plughubs 21-24 of rows 1 and 2 for typewriter I, of rows 8 and 9 for type-
writer n.
The print step counter and print counter are reset simultaneously. Six column selection plug-
hubs'are left^blank after the last tab and then the reset is plugged. The reset plughub is the
25th plughub of row 2 for typewriter I and of row 9 for typewriter II.
1. The operating decimal point lies between columns 15 and 16. Plug typewriter I to print
quantities, which may be positive or negative, to 8 decimal places, grouped by threes to
the right and left of the decimal point, argument control after 2 decimal places.
COL-SEL-PRINT-1 1
Row 2
Row 3 ooooo
o i I i • •— • • • •
RO
PRINTJcjrR-RO
15 10
ooooo
45 49
M
• •-"% ooooo
RO-CONTROL-RELS
10
Row 4
25 24
C
2524
Row 6 • o o o o ooooo ooooo ooooo ooooo
2524 20 15 10 5 (4-5)
Row 18 ooooo ooooo ooooo ooooo oooo • —
2 1
The operating decimal point lies between columns 21 and 22. Plug typewriter II to print
quantities, which may be positive or negative, to 21 decimal places, digits in groups of 3,
5, 5, 5, 3 to the right of the decimal point.
PRINTING
277
DP TAB
Row 8 • • • o o o~
Row 9
25
R
-•
25
21
TAB
o o o o
21
Row 10 ooooo
Row 11 o •— {
25 24
C
Row 12 •-•
25 24
V
COL-SEL-PRINT-2
10
20
25
I SPACES |_L___r
* o o o o • t O 1
"I o o o o
30
o o o • o
40
PRINT-CTR-RO
19
o • o o o
35
39
ooooo
45 49
£
=5=
20
15 10 5
RO-CONTROL - RE LS
00 ooooo ooooo ooooo ooooo
20 15 10 5
13 90000 ooooo oooo
Row LO »oooo ooooo ooooo ooooo ooooo
2524 20 15 10 5 (4-5)
Row 18 ooooo ooooo ooooo ooooo ooooo
2 1
3. The operating decimal point lies between columns 15 and 16. Plug typewriter I to print
all 23 digits of quantities, positive or negative, grouped by fives to the right and left of the
decimal point, argument control after 2 decimal places.
DP TAB
Row 1 •"
COL-SEL-PRINT-1
25
• 00 o •— •■
21
R TAB
Row 2 !-• o o o o
25 21
Row 3 ooooo
•— • p • • f • • h
/?
20
SPACES
9
Row 4 o
10
25
• o o o •
T{ • • • P~9~
15 f 19
PRINT-CTRJ-RO |
• oooo oio
30
35
o o o • o
40
o o
39
ooooo
45 49
♦-• •— •-
-•— •
2524 20 15 10 5
C RO-CONTROL-RELS
Row 5 •— • 000 OOOfO ooooo ooooo ooooo
15 10 5
25 24
20
Row 6 »oooo ooooo ooooo ooooo ooooo
2524 20 15 10 5 (4-5)
Row 18 ooooo ooooo ooooo ooooo oooo • —
2 1
278
PLUGGING INSTRUCTIONS
(ii) The first ten plughubs of rows 38 and 39 control the vertical grouping of quantities printer on
typewriter I. The second set of ten plughubs on the same rows serve the same purpose *or
typewriter II. The vertical spacing of each typewriter is under control of the read-out of a
line step counter (LSj andLS 2 ). These counters step every time a carriage return occurs.
Various vertical groupings are possible but the pattern must repeat in groups of ten lines or
less. At the end of the desired grouping, the line step counter must be reset. This reset is
obtained by connecting plughub R (6 for typewriter I, 16 for typewriter II in row 39) to the line
step counter read-out. When the step counter resets, a single line space is obtained. If an
extra vertical space is desired, one of the extra space plughubs (1-5 for typewriter I, 11-15 for
typewriter II in row 39) must be plugged to the step counter read-out.
Plug typewriter I for vertical groups alternately of 3 and 4 quantities. Plug typewriter II
for vertical groups of 8 quantities.
Row 38 ooooo
9 in
7 6 5
ooooo
4 3 2 1 10
o o
9 8
o o o
2 1 10
Ro^
EXTRA SP 2
• oo o •
[7 6 5 4 [3
OGw 0^0 OO
R EXTRA SP 1
5. Plug typewriter I for vertical groups of 4 quantities. Plug typewriter II for vertical groups
of 5 quantities.
Row 38
Row 39
ooooo o o o o • ooooo ooooo •
9 8 7 6 5\ 4 3 2 1 10 9 8 765/4
ooooo o o o o • ooooo ooooi o
o o o o
3 2 1 10
ooooi ooooo
R EXTRA SP 2 R EXTRA SP 1
(12) The print counters may be plugged for a "half pick-up" which adds or subtracts five in the
column to which it is plugged, according as the quantity in the print counter is positive or nega-
tive. Note that the typewriter reverse switches do not change over the half pick-up, which is
not reversed but continues to add into the print counter for which it is coded and plugged. The
half pick-up impulse plughubs lie in rows 6 and 13 for print counters I and n respectively,
labeled IMPULSE 1/2 CORR. The impulse plughubs are plugged to rows 7 and 14 for print
counters I and II respectively, labeled CTR.
6. The operating decimal point lies between columns 15 and 16. Plug print counter I for a half
Dick-uo correcting the eighth decimal place.
Row 6 o
2524
Row 7 o •-
24
20
15
10
20
15
10
4 1/2 CORR
(4-5)
CTR
The operating decimal point lies between columns 19 and 20.
half pick-up correcting the tenth decimal place.
Plug print counter II for a
PRINTING
279
Row 13 o
2524
Row 14 o •— (
24
20
20
15
10
15
10
~i 1/2 CORR
(4-5)
CTR
8. The operating decimal point lies between columns 15 and 16. Plug print counter and type-
writer I to print on the same horizontal line:
(a) an argument, zeros dropped off after 2 decimal places,
(b) a positive or negative quantity to 10 decimal places, digits grouped by fives to the right
and left of the decimal point, half pick-up correcting the tenth decimal place.
Plug the line step counter for vertical groups of six lines.
Row 1
Row 2
DP TAB COL-SEL-PRIN T-1
* • O O O O • » | |H| • • • f • • * *7-* f • f •
25
21
R TAB
-•0000
25 21
Row 3 ooooo
Row 4 o
•—♦
20
z\
SPACES
ooooo
K
o o
25
-• • fer*
15
o o
o o • o
O OfOOO
30
1
O o o o o
40
19
ooooo
35 39
ooooo
45 49
PRINT-CTR^RO
2524
20
15
10
■•— • ooooo
5
Row 5
Row 6
Row 7
Row 18
Row 38
Row 39
c
•— • o o
2524
o <
20
RO-CONTROL-RELS
10 ooooo ooooo
15 10
HyT mn. stt. 1 f>. rro?R
ooooo
5
, 1
25 24
20
15 10
COUNTER
5
(4-
24
20
15 10
5
ooooo ooooo ooooo ooooo 0.09-
2 1
ooooo ooooo ooooo ooo»-
98765 4321 10 987 6
OOOOO OOOOO OOOOO 00
R EXTRA SP 2
o ooooo
5 4 3 2 1 10
■• ooooo
R EXTRA SP 1
280
PLUGGING INSTRUCTIONS
successive digits unless there is already a space, a decimal point or an argument control plug-
ged between them.
9. The operating decimal point lies between columns 15 and 16. Plug typewriter II to print in
half time, positive or negative quantities, to 8 decimal places, digits grouped by threes to
the right and left of the decimal point, argument control after 2 decimal places, half pick-
up to correct the eighth decimal place. Plug the line step counter for vertical groups of
five lines.
Row 8
Row 9
DP TAB
* • • o o
COL-SEL-PRINT-2
25
R
21
TAB
r* o o o o
. 25 2
21
Row 10 o o o o o
Row 11
Row 12
Row 13
o
2524
°^ ]°A\Y? ioTV%°
V \T
20 > >
SPACES
o o lo o
&
25
• • o
*
| PRINT-CTR-ROl
i i » t till <\ J
30]
7-.
40
/
\
t
20
2524 20
Lfi
* o o
10
o o
35
o o
45
o o
5
19
39
• o o
49
RO-CONTROL-RELS
• O OOOOO OOOOO 00000
15 10 5
Row 38 ooooo oooo^ ooooo ooooo ooooo
8 765 4321' 10
Row 39 o
9876 5N432110 9
oooo oooo# ooooo o
R EXTRA SP 2
oooo ooooo
R EXTRA SP 1
(14) The "Typewriter Reverse Switches" are located to the left of the sequence mechanism. It should
be noted that, as stated in note (12), though these switches reverse the codes of the print counters
and the codes initiating printing, they do not reverse either the plugging or the half pick-up
coding.
281
SAMPLE PLUGGING
The plugging of the calculator is shown for operating decimal point between columns 15 and 16.
Division is plugged to provide 7, 14 or 22 digits in the PQ counter under control of Miscellaneous
codes 643, 6431 and blank respectively.
Interpolator I is plugged for afunctional tape in which Aa = 0.1, highest order "h" = 14 and
the tape decimal point lies between columns 15 and 16.
Interpolator III is plugged for a functional tape in which Aa = 0.01, highest order "h" =13 and
the tape decimal point lies between columns 9 and 10.
Typewriter I is plugged for positive or negative quantities, all 23 columns of digits grouped by
fives to the right and left of the decimal point, argument control after 2 decimal places. Line step
counter 1 is plugged for vertical groups of six lines.
Typewriter n is plugged for positive or negative quantities, digits grouped by threes to the
right and left of the decimal point, argument control after 2 decimal places, half pick-up to correct
the eighth decimal place. Line step counter 2 is plugged for vertical groups of five lines.
The following switch settings must be made:
Divide N minus decimal switches = 07;
Log N value switches = 07;
Interpolator I, push button switches = 0051 , dial switches = 3;
Interpolator III, push button switches = 0044, dial switches = 5.
Interpolator II reads a value tape and therefore requires no plugging. The card feed and card
punch pluggings are assumed to be direct and are not shown.
282
PLUGGING INSTRUCTIONS
MP-DIV PLUGBOARD
Row 1
Row 2
Row 3
Row 4
Row 5
Row v
Row 7
Row 8
Row 9
Row 10
Row 11
Row 12
o • o o ooooo
* o * o "o ooooo i oooo ooAoo ooooo PLACE LIM.
23 20 15 10 5
25
20
ooooo ooooo ooooo PQ CTR
15 10 5
OfOOO OOOOO 00
46 45 40
35
30
PQCTR
o 1 » » > — =• — t — c — 1 — • — • — > • • — • • — • — • — • — * ' * — • — • — •—• P-OUT
24 20 15 10 5
* - - ■ ■ * • n tttt- • • • • • C-VAL-1
24 20 15
„a ^ ^ ^ -~--Q J i — *■ *' ■ ■ ^—- ^ i — 5 ' *
10
BUSS
OA
9.n
1 R
m
5
ooooo ooooo ooooo ooooo ooooo BUSS
24 20 15 10 5
ooooo ooooo ooooo ooooo ooooo C-VAL-2
24 20 15 10 5
[24
o >•
20
15
10
C-VAL-3
BUSS
24
20
15
10
ooooo ooooo ooooo ooooo ooooo BUSS
<£u
10
ooooo ooooo ooooo ooooo ooooo I-IN-1-2
6 5 4 3 2 1
Row 13 o » •— •
now i.'i
Row 15
Row 16
Row 17
Row 18
[6 5 4 3\ 2 1
o^uou uuu
24 20
•— • OOO OOOOO OOOOO OOOOO i-lJN-i-iS
r\ r\ r\ r\ n r\
n RTTRS
15
10
OOOOO OOOOO OOOOO OOOOO OOOOO BUSS
24 20 15 10 5
ooooo ooooo ooooo ooooo ooooo INT-IN-3
24 20 15 10 5
ooooo ooooo OO
24 20 15
OOOOO OOOOO OO
24 20 15
10
INT-IN-4
BUSS
10
283
SAMPLE PLUGGING
MP-DIV PLUGBOARD (continued)
Row 19 o o o o o ooooo •— <
24 20 15
10
BUSS
Row 20 ooo
24 22 20
i • • • • — • • • o o ooooo 1/2 T
15 10 5
Row 21 ooooo ooooo ooooo ooooo. ooooo H-CORR-2-2
24 20 15 10 5
Row 22 ooooo ooooo ooooo ooooo ooooo INT
24 20 15 10 5
Row 23 ooooo ooooo ooooo ooooo ooooo INT
24 20 15 10 5
8
Row 24 ooooo ooooo ooooo ooooo ooooo H-CORR-2-3
24 20 15 10 5
Row 25 o
Row 26 o
24
20
-•— ♦ ooo ooooo ooooo H-CORR-3-2
15 10 5
24
20
-•— • ooo ooooo ooooo INT
15 10 5
Row 27
Row 28
0/» <
24
o t
24
20
15
10
20
15
INT
H-CORR-3-3
10
284
PLUGGING INSTRUCTIONS
FUNCTIONAL PLUGBOARD
DP TAB
Row 1 *t? o o o •— »
Row 2
L
R TAB
oooo
Row 3 ooooo
#—• » •— •
A
20
SPACES
oooo
51 m * •-^-
1° 1
25
10 1 15 n
i - "^ oooo o • o
>• o o o •
ss
30
35
o o o|# o
40
Row 4 o • • '• • •— •
24 20
C
Row 5 •— • o o o ooo
25 24 20
•-L • • • • •— »
15 10
oooo
45
*— • • • • • •
o ooooo ooooo ooooo
15 10 5
TYPEWRITER I
COL-SEL
i, n n n n n r> n n d OOOOO 00000 OOOOO
2524" 20 15 10 5 (4-5)
Row 7 ooooo ooooo ooooo ooooo ooooo
24 20 15 10 5
DP TAB
Row 8 i ? 9-j o o o •— <►
_ 1
TAB!
Row 9 $0000
Row 10 ooooo
\ 5 1 ] f 10
=r~» «-r» * f >• •y*
20
SPACES
o • o
o 4
oooo
25
15
• o |o |o O 00
30
•— •
20
o o o • • o o
40
f o
35 ii
o o oooo
45
15 1_
10
oo ooooo
5
Row II o •— •— • •
24
C
Row 12 •-• O O OOOfO ooooo ooooo ooooo
25 24 20
PRINT CTR-RO
RO-REL8
1/2 CORR
CTR
TYPEWRITER II
COL-SEL
To o (
15
10
Row 13
2524
Row 14 o •—
20
TT
10
15
10
• • • • • 1
5 1 (4-
J~tI
24 20
Row 15 o m • • * — •-• ooo ooooo ooooo ooooo
Row 16
O j» > 9 # ■ •— • OOU UUUUU u v v v «
(6 5 4 3\2 1
o * o o o o • • • I — •— • ooo ooooo o
oooo
24 20 15 10 5
Row 17 ooooo ooooo ooooo ooooo ooooo
Row 18 ooooo ooooo ooooo ooooo o o o • •-
PRINT CTR-RO
RO-RELS
1/2 CORR
CTR
I-IN-1
BUSS
SAMPLE PLUGGING
FUNCTIONAL PLUGBOARD (continued)
285
Row 19 o
Row 20 o
24
20
-•oooo ooooo ooooo H-CORR-2
15 10 5
24
20
-•oooo ooooo ooooo INT-IN-2
15 10 5
Row 21
Row 22 L.
24
8
o I
24
20
I,
15
10
20
15
10
Row 23 ooooo ooooo o<
24 20 15
Row 24 ooooo ooooo oi
24 20 15
10
10
Row 25 o m • • • '• • • •— • •— •-
24 20 15
Row 26 o>» • • • — • • • • • — •-4-
24 21 20 15
10
10
Row 27 oy
24 21 20
Row 28 o^«ooo ooo
24 20
15
10
o ooooo
5
o ooooo
5
15
10
Row 29. 0'
24
20
15
10
Row 30
25
21 20
15
10
o ooooo
5
Row 31 ooooo ooooo ooooo ooooo o > • ' • •
45 40 35 30
Row 32 o
Row 33 o
24
20
15
10
24
20
15
10
Row 34 ooo
24 22 20
15
10
ooooo
5
Row 35 ooooo ooooo •-<
24 20 15
10
INT-IN-2
H-CORR-3
INT-IN-2
BUSS
BUSS
LIO-OUT
EIO-IN
BUSS
BUSS
EIO-OUT
EIO-OUT
SIO-IN II
BUSS
BUSS
SIO-OUT-I
286
PLUGGING INSTRUCTIONS
niT»TrtnWA\l»I T>T Ttpt)A»DT\ fnnrvH miafl\
Row 36 o
Row 37
't
o >•
24 22 20
15
10
o O
5
24
Row 38 o o o o o
Row 39 o o o o o
Row 40 • • •' • •
20
o o o o •-
9 8 7 6 5
15 10 5
OOOOO 000 »-i0 o o o o o
4321 10 987 65 4321 10
0000»— 'OOOOO OOO 1 -* OOOOO
R R
SIO-OUT-n
BUSS
OOO OOOOO oooo
10 io
9's
287
CHAPTER VI
SOLUTION OF EXAMPLES
In most cases there are several methods of adapting a problem for machine computation. After
all methods of attack have been considered, one usually will show distinct advantages as regards
speed and ease of operation and reliability of the checking procedures employed.
Since machine time is extremely valuable, the first consideration in planning a sequence tape is
to reduce the computation time to a minimum consistent with the required accuracy. However, a fine
balance must be maintained between computation time and the ensuing complexity of the coding. The
conservation of one or two cycles of machine time will, for example, not be profitable if it means that
the counters containing essential parts of a computation must be reset before the results are checked.
The second consideration in planning a computation is ease of operation. If switches must be
altered or sequence tapes interchanged at relatively short intervals of time, these operations will
constitute not only a loss of time but also a source of error.
Ease of rerunning a computation in the wake of an error and the possibility of computing for
specific values of the independent variables must also be considered. Machine failures occur from
time to time. The amount of time consumed in detecting the source of an error is usually dependent
upon the complexity of the coding. The time required to resume operation after an error, which is
dependent upon the number of manipulations the attendant must perform, should be reduced to a mini-
mum in a well planned sequence tape. Specifically, no decisions or computations should be required
on the part of the attendant. The operating instructions and the values printed or punched should pro-
vide all the information necessary for rerunning any part of the computation.
Finally, of paramount importance in the design of a sequence control tape are the checks on the
computation. These must insure positive proof that the output values obtained are precisely those
required and that they are correct to the desired accuracy. Four classes of errors must be taken
into account: (1) errors inherent in the mathematical formulae; (2) errors produced by a repetition
of the four fundamental operations of arithmetic; (3) errors introduced by manual operations; (4) errors
due to mechanical or electrical failures within the calculator itself.
288
SOLUTION OF EXAMPLES
. . n jl_. „i J- i~„ *-,,.„+ ks oTTiinqtori rfufintr the nreliminarv
The errors inherent in tne mamemaucai wruimac muo«. u e cro^ud^u -u- — -i— *.
analysis before the coding is begun. Decisions must be made as regards the number of terms of an
infinite series to be retained, the number of times an iterative process must be applied and the order
of interpolation required. These decisions are dependent upon the interval and increment of the inde-
pendent variable and the accuracy desired in the computed results.
The loss of accuracy due to the repetition of the four basic arithmetical operations in a finite
digital calculator must be subjected to a detailed analysis. For each operation, the maximum error
must be assumed and the error of the final result computed. The simple expedient of using a certain
number of extra computing columns will, in general, nullify errors from this source. Thus the choice
*e tn a nnara Hn<T H B ~ m5 ! no<*iiinn nrfll in tsart be dictated by the number of extra columns so allowed.
The two sources of human error mentioned in Chapter V, incorrect switch settings and incorrect
plugging, are perhaps the most serious of all. If the mathematical nature of a problem permits a
check of the final results, independent of the method of computation, the errors of the manual oper-
ations will be detected. If, however, the only checks which may be applied are those of an operational
character; i.e., substantiating the fact that the desired sequence of operations has been correctly
performed by the calculator, such errors as incorrect switch settings may not be detected. Hence
meticulous precision on the operator's part and careful checking of all manual operations are essential.
Mechanical and electrical failures within the calculator itself are the final source of errors
which must be checked. If a problem is properly coded, either operational or end result checks must
be provided to detect such failures. In no case should the calculator be permitted to run more than
twenty minutes without checks .
Although the probability is exceedingly small, a failure in the checking circuits of the machine
may occur. To provide for the detection of such an event, all check quantities should be printed and
kept under observation. If the check quantities are printed before the checking operation is performed,
in case of failure, the magnitude and conformation of the error may provide a clue to its source. If
possible, all quantities essential to the computation of the value being checked should be preserved
in the calculator until the check is completed. These quantities may then be printed or punched and
manual computation used to aid in tracing the source of the error. If the length of a computation is
289
SOLUTION OF EXAMPLES
not too great, a rerun after a failure, with the tolerances set arbitrarily low so that the machine will
stop even though the computation is correct, may provide correct values for comparison with those
in error. Such a comparison will often lead directly to the particular source of difficulty.
Before the actual coding is begun, the storage counters should be allocated to the various parts
of the computation. Then as the coding proceeds, a diagram should be prepared showing the lines of
coding by which the counters are reset and the quantities they contain at every cycle of the computation.
A clear copy of the coding must be provided before an attempt is made to run a sequence tape
on the calculator. The lines of perforations in the tape should be numbered to correspond to the lines
of coding. In the coding sheets, colored indicators should call attention to all prints, interpolations
and checks. All functional operations should be separated by horizontal rulings.
Before a sequence tape is run on the machine, a manual computation of a degenerate case, of the
first point to be evaluated or of some arbitrary point, should be made. Comparison of the results of
this manual computation with the results yielded by the tape will serve to check the coding and punch-
ing of the tape. The manual computation should parallel the operations dictated by the tape so that
intermediate results may be compared if the final results fail to check.
Every sequence control tape must be accompanied by operating instructions. These instructions
must be sufficiently complete to enable an experienced attendant to set up the problem and operate the
calculator. All value and functional tapes and cards supplied with a problem must be thoroughly
checked before a problem is ready to run. The only remaining source of input values, the switch
settings, must be checked just before the machine is started. Directions for checking the switch set-
tings must be given in the operating instructions. The quantities standing in the switches must be
printed or punched for checking, either under control of a sequence tape or under manual control of
the keyboard ordinarily used in the preparation of sequence tapes (see page 45, last paragraph). If
blank tape is placed across the reading pins of the sequence mechanism, this keyboard maybe connec-
ted to the calculator to transmit successive single lines of coding to the machine. Only an experienced
attendant should attempt to use the keyboard, however, because of the rapid manipulations necessary
in using automatic codes. The keyboard is most frequently used for printing and punching quantities
when testing to locate a source of error.
290
SOLUTION OF EXAMPLES
It is often necessary to make preliminary computations and to set certain values in storage
counters before a computation is begun. In such an event a starting tape is used. It is usually a short
two-ended control tape and may well include printing quantities from the switches, checking plugging
and resetting storage counters. If possible starting tapes should be used only at the beginning of a
problem or to re-establish operation after failure to check. In general, they should not be used at the
start of each individual run since too much time would be wasted in changing control tapes.
The operating instructions accompanying a sequence tape must include all of the following in-
formation.
(1) Switches.
All quantities to be set in switches must be listed. Both symbols and numerical values must
be stated. All tolerances must be accompanied by a reference to the quantity to be checked.
(2) Tapes.
All value and functional tapes, together with a statement of the interpolator on which they
are to be placed, must be listed. All tapes must be clearly labeled and starting lines indi-
cated. On the sequence tape itself, the starting line and ail rerun lines must be marked.
(3) Card Feeds.
The cards required by each feed must be identified by their serial numbers. The relation-
ship of the serial numbers to the argument and function being computed must be clearly
stated. In the instructions for reruns or any other special runs, further instructions for
the replacement oi car^s mus*. *>e given.
(4) Card Punch,
The quantities being punched and the printed values with which they may be compared must
be identified. The composition of serial numbers in relation to the argument and function
must be made clear. Instructions must be given for the labeling, filing and storing of all
cards punched.
(5) Typewriters.
The mathematical symbols of the quantities printed and their relative positions must be
stated. Sample headings of pages or rolls should be cited. It must also be stated whether
291
SOLUTION OF EXAMPLES
or not the typewriter reverse switches may be used since these switches do not reverse the
half pick-up coding.
(6) Storage Counters.
All manual resets of storage counters must be listed. In particular, if a counter is used to
accumulate for each quantity or group of quantities printed, and stop the machine at the end
of a page, this counter must be identified.
(7) Functional Counters.
All manual resets required must be listed.
(8) Checks.
All checks must be listed and the following information supplied for each check:
(a) quantity checked;
(b) amount of tolerance and switch from which it is derived;
(c) line of coding containing the check procedure;
(d) procedure in case of failure to check.
(9) Rerun Instructions.
In general, these will be of two types:
(a) rerun of the point on which the failure occurred;
(b) rerun of any other point.
Complete plugging instructions must also accompany every sequence control tape. These in-
structions must include all of the following information: (1) a statement of the position of the operating
decimal point of the calculator and of the typewriter and punch decimal points, if these differ; (2) a
list of the units of the calculator employed in the computation and diagrams of their plugging; (3) the
switch settings for division, logarithms and interpolation must be listed if these functions are to be
used; (4) for each typewriter, the horizontal grouping of the digits to be printed must be stated, the
vertical grouping of the lines of the tabular values must be given, plugging diagrams for each type-
writer must be provided.
If the logarithm, exponential, sine or interpolator units are to be used by a sequence tape, these
units should be tested on known arguments before the tape itself is tested. Such known arguments
292
SOLUTION OF EXAMPLES
musi inciuae, ior tile exponential anu sine units, doui puaiuvc auu ncgauVc miuci), «• "«c ^a^e ^i —.-
sine unit, arguments from each of the four quadrants using both the sine and cosine series should be
chosen. The reading pins of the interpolators should be tested by reading known values such as di-
agonal numbers .
If a sequence tape is of such general interest that it will be preserved in the tape library, its
starting tape should be designed with care in order to check all switch settings, all plugging and all
of the functional units employed, as well as to compute the initial values required by the main control
tape. However, for problems to be run but once on the calculator, the starting tape should be as
simple as is consistent with adequate provision for setting up the problem and rerunning in case of
failures s
In the preparation of control tapes and operating instructions, a standard practice is necessary
since the operation of large scale calculating machinery on a continuous basis is of necessity a group
enterprise. The methods and techniques employed must be standardized in order that the required
results may be obtained with a minimum of special instructions. The foregoing discussion covers the
more important rules of coding developed in nearly two years of operation of the calculator. However,
so brief a description cannot be expected to cover all the details involved. These will be illustrated
by means of examples chosen for mathematical simplicity in order that the coding and checking may
be the focal points of the discussion.
Example 1. It is required to evaluate the polynomial,
F(x) = x 4 + 3x 3 - 3x 2 /4 - 22x + 3,
by successive multiplications, in the interval 5 < x £10, with ax = 0.01. The values of F(x) are to
be punched in tabulating machine cards for use in further computation. Each card must be identified
by a serial number consisting of the argument, x n , punched with decimal point between card columns
75 and 76 (machine columns 5 and 6) and a one in the 80th card column (1 in 1st machine column). It
is not required to print the values of F(x). One value of F(x) is to be computed during each revolution
of the control tape. The tape is to be designed so that it may be rolled back and rerun without any
additional manipulations. The starting tape is to be designed so that it may be used to re-establish
the computation for any arbitrary value of the argument.
293
SOLUTION OF EXAMPLES
If F(x) is written in the form,
F(x) = (((^ + 3^ - 3/4)x n - 22)^ + 3,
it should be clear that only three multiplications will be required to evaluate the given polynomial. In
general a polynomial of nth degree will require not more than n multiplications. The constants will
be supplied from switches. Since F(x) < 2 x 104 in the interval under consideration, the standard
position of the operating decimal point, between columns 15 and 16, may be assumed.
Switch Settings
No.
1
2
4
5
6
7
9
10
11
Code
741
742
743
7431
7432
74321
751
752
7521
Setting and Purpose
a x = 1 in 14th machine column; increment of argument for computing
ax = 1 in 4th machine column; increment of argument for punch card serial
numbers
1 in 1st machine column; punch card code for F(x); zero check tolerance
0.75
22
3
x n-l = argument for computing; decimal point between columns 15 and 16; used
in starting tape only
x n-l + 3 ' de cimal point between columns 15 and 16; used in startingtape only
x n _ 1 = argument for punch card serial numbers; decimal point between col-
umns 5 and 6; used in starting tape only
Since the argument is always £ 5, containing at least one non-zero digit, and is always used as
the multiplier, four lines of coding may be interposed between the read-in of MP and the read-out of
the product. The resets of the counters receiving the products, and the additions of the successive
constants, are interposed in the multiplications.
Starting Tape
reset ctr. 1
x n-l * rom sw. 9 to ctr. 1; argument for computing
Line
OUT
IN
MISC.
1
1
1
7
2
751
1
7
294
SOLUTION OF EXAMPLES
reset ctr. 2
x - + 3 from sw. 10 to ctr. 2
n-1
reset ctr. 64
x ., from sw. 11 to ctr. 64; argument for punch card serial
n_1 number
Main Control Tape
ax from sw. 1 to ctr. 1; ctr. 1 = x - + ax = x ; argument for
computing
ax from sw. 2 to ctr. 64; ctr. 64 = x n-1 +ax = x n ; argument
for punch card serial number
ax from sw. 1 to ctr. 2; ctr. 2=x^ *+ax + 3=x+3
n- 1 n
x n + 3 from ctr. 2 to MC
x from ctr. 1 to MP
re»et ctr. 3
- 0,75 from sw, 5 to ctr, 3
(x + 3)x to ctr. 3; ctr. 3 = (x + 3)x - 0.75
v n ' n n n
(x n + 3^ - 0.75 from ctr. 3 to MC
Rerun line
x„ irom cir. i 10 mr
n
reset ctr. 4
- 22 from sw. 6 to ctr. 4
((x n + 3^ - 0.75)x to ctr. 4; ctr. 4 = ((x + 3)x - 0.75)x n - 22
Line
OUT
IN
MISC,
3
2
2
7
4
752
2
7
5
7
7
7
6
7521
7
7
i
741
1
7
rtAn
f±£i
n
i
i
3
i
741
1
2
7
1 \
4
1 1
2
761
7
5 1
7
6 1
7
1
7
8
7
9
7
in
21
21
n i
■
11
7431
21
32
12
21
7
13
21
761
7
14
7
15
1Q
■t
i.
7
17
7
18
7
19
3
3
7
20
7432
3
32
i 2i
3
7
SOLUTION OF EXAMPLES
295
((x + 3k - 0.75k - 22 from ctr. 4 to MP
« n n
x n from ctr. 1 to MP
reset ctr. 5
3 from sw. 7 to ctr. 5
(((x n + 3)x n - 0.75k - 22)x to ctr. 5; ctr. 5 = F(x )
F(x n ) to punch ctr.
initiate punching and wait until punching is completed
x n from ctr. 64 to punch ctr. for serial number
1 in 1st machine column to punch ctr.; code for F(x)
initiate punching and continue operation
Line
OUT
IN
MISC.
22
3
761
7
23
7
24
25
1
7
26
7
27
7
28
31
31
7
29
74321
31
30
31
7
31
31
753
32
51
33
7
753
34
743
753
35
75
36
87
Operating Instructions
(1) Set switches as listed. Punch the values set in the switches and compare the punched values
with the list of switch settings.
(2) The quantities punched under control of the main tape are the values of F(x ). Each card is to
be identified by a serial number consisting of the argument, x , punched in card columns 74-77
and a one, the code for F(x), in card column 80. All cards punched are to be placed in the
drawer provided for this purpose.
(3)
(4)
Run starting tape .
Run main control tape. If no failures occur, continue running until card for x =9.99 has been
punched, then press stop key. n
(5) If a failure occurs during the computation for the argument, x, roll the tape back to line 4
marked "Rerun line", and repeat the computation for this value. '
(6) If tests are made and counters disturbed, or if it is desired to compute for any arbitrary value
of the argument, repeat the starting procedure with switches 9, 10 and 11 reset as listed.
296
SOLUTION OF EXAMPLES
\iy OiliCc uic iiictAiiliuin liuHiuGJi ux iiuu~zici> vj> ui^ito lu clIIj on. gwm.JtS.iJ.*. xu wuuuj me iAiuAkuim&t *.*.*.** v * v *
tape may be computed as follows:
accumulate arguments 3
three multiplications 30
punching of results 10
punching of serial number _3
46 cycles = 13.8 seconds.
If further computations are added to this tape, it will be possible to interpose thirteen of these
cycles reducing the computation time to 9.9 seconds,
(8) The first card punched under control of the main tape will be F(x) = 874.25 with the serial num-
ber 500001.
Plugging Instructions
(1) Plug the multiply unit for the standard position of the operating decimal point (see page 247).
(2) Plug the punch as shown in the diagram below.
PUNCH MAGNETS
10 15
20
I 25
• •' • •
45
0000 0000
65
0000 0000
COMP MAG
2A 2B 4A
30 35 40
0000 0000 0000
50 55 60
oooo oooo oooo
70 75
oooo o •-
•— •■
80
OR CTR TOT EXIT OR M S IN
4B 6A 6B
6B
9 . > 9 0000 0000 0000 0000
Example 2. It is required to evaluate the polynomial of example 1 using difference engine techniques.
Suppose five values of the function, F _, F ., F «, F „, F _-, to be available in punched
cards. A starting tape will be designed to feed these five cards, and compute the differences asso-
ciated with the argument x n _j. Switch 8 will contain a 4 F = 0.000 000 24 and this quantity will be used
297
SOLUTION OF EXAMPLES
to check the differences computed by the starting tape . Before beginning the computation with the
calculator, F(4.95), F(4.96), F(4.97), F(4.98) and F(4.99) must be computed manually and punched in
tabulating machine cards. Thereafter, F(x) must be punched in cards by the main control tape.
Hence, in the event of a machine error, any five successive values of the function, known to be cor-
rect, may be used to re-establish the computation with the aid of the starting tape.
The main control tape is to be designed so that the value of the function and its differences com-
puted in the m-lst revolution of the tape will be used in the mth revolution of the tape to compute the
next succeeding value of the function and its differences. The standard decimal position will be used.
Starting Tape
reset ctr. 1
F K to ctr. 1 from card feed I
n-o
reset ctr. 2
F . to ctr. 2 from card feed I
n-4
reset ctr. 3
F . to ctr. 3 from card feed I
n-o
reset ctr. 4
F to ctr. 4 from card feed I
n-2
reset ctr. 8
F , to ctr. 8 from card feed I
n-1
reset ctr. 9
F i from ctr. 8 to ctr. 9
- F n _2 from ctr. 4 to ctr. 9; ctr. 9 = a F «
- F „ from ctr. 3 to ctr. 4: ctr. 4 = a F „
n-3 ' n-3
- F . from ctr. 2 to ctr. 3; ctr. 3 = a F .
n-4 ' n-4
- F„ ,- from ctr. 1 to ctr. 2; ctr. 2 = a F c
n-o n-o
reset ctr. 10
a F „ from ctr. 9 to ctr. 10
n-^
Line
OUT
IN
MISC.
- 1
1
1
7
2
1
7632
3
2
2
7
4
2
7632
5
21
21
7
6
21
7632
7
3
3
7
8
3
7632
9
4
4
7
10
4
7632
11
41
41
7
12
4
41
7
13
3
41
732
14
21
3
732
15
2
21
732
16
1
2
732
17
42
42
7
18
41
42
■'"■ ' — I
7
298
SOLUTION OF EXAMPLES
- a F „ from ctr. 4 to ctr. 10; ctr. 10 = a 2 F„ «
n-o ti-o
- a F A from ctr. 3 to ctr. 4; ctr. 4 = a 2 F
n-4 n-4
- a F c from ctr. 2 to ctr. 3; ctr. 3 = a 2 F c
n-5 ' n-5
reset ctr. 11
o
a F from ctr. 10 to ctr. 11
n-o
- a 2 F . from ctr. 4 to ctr. 11; ctr. 11 = a 3 F .
n-4 ' n-4
- A 2 F rif; from ctr. 3 to ctr. 4; ctr. 4 = A 3 F nR
reset ctr. 12
" * n-4 " v "' * s ** w v '** ' *"
- A 3 F c from ctr. 4 to ctr. 12; ctr. 12 = A 4 F
n-o
reset comparison ctr. 5
A F from sw. 8 to ctr, 5
n-5
-A*F
from ctr. 12 to ctr. 5
n-5
reset check ctr . 72
zero check tolerance from sw. 4 to check ctr. 72
A 4 F - a 4 F| to check ctr. 72
check; reset check ctr. 72
reset ctr. 64
x 1 from sw. 11 to ctr. 64; argument for punch card serial
number
Main Pnntrnl Tanp
reset working counters for differences computation
transfer differences from storage to working counters
n-1
a F n5! from ctr. 9 to ctr. 13
Line
OUT
IN 1
MISC.
19
3
42
732
20
21
3
732
21
2
21
732
22
421
421
7
23
42
421
7
24
3
421
732
25
21
3
732
26
43
43
7
27
421
43
7
28
3
43
732
29
31
31
7
30
75
31
7
31
43
31
732
32
|74
74
7
33
j 743
74
7
_Hj
1"
74
71
35
74
74
64
36
7
7
7
37
7521
7
7
1
I 43
43
7
2
431
431
7
3
432
432
7
4
J4321
4321
7
I 4
43
1
6
I 41
11
431
7
SOLUTION OF EXAMPLES
299
a 2 F n from ctr. 10 to ctr. 14
n-3
3
A F n4 from ctr. 11 to ctr. 15
4 4
a F from sw. 8 to ctr. 15: ctr. 15 = a°F
n-o
a 3 F , from ctr. 15 to ctr. 14; ctr. 14 = a 2 F „
2
a F 9 from ctr. 14 to ctr. 13; ctr. 13 = a F „
a F . from ctr. 13 to ctr. 12; ctr. 12 = F
n-i n
F from ctr. 12 to punch ctr.
n
reset ctr. 8; initiate punching; continue operation but complete
punching before reading into punch ctr.
reset ctr. 9
reset ctr. 10
reset ctr. 11
ax from sw. 2 to ctr. 64; ctr. 64 = x 1 +ax = x ; argument
for punch card serial number n
F n from ctr. 12 to ctr. 8
a F . from ctr. 13 to ctr. 9
n-2
3
a F n3 from ctr. 15 to ctr. 11
x n from ctr. 64 to punch ctr. for serial number
1 in 1st machine column to punch ctr.; code for F(x)
initiate punching and continue operation
Line
OUT
IN
MISC.
7
42
432
7
8
421
4321
7
9
75
4321
7
10
4321
432
7
11
432
431
7
12
431
43
7
13
43
753
7
14
4
4
751
15
41
41
7
16
42
42
7
17
421
421
7
18
742
7
19
43
4
7
20
431
41
7
21
432
42
7
22
4321
421
7
23
7
753
24
743
753
25
75
26
87
Operating Instructions
(1) Set switches as listed on page 293, adding switch 8 = 0.000 000 24. Punch the values set in the
switches and compare the punched values with the list of switch settings.
(2) The quantities punched under control of the main tape are the values of F(x ). Each card is to
be identified by a serial number consisting of the argument, x , punched in card columns 74-77
and a one, the code for F(x), in card column 80. All cards punched are to be placed in the
drawer provided for this purpose.
(3) Five cards, labeled "starting cards", must be placed in card feed I. These cards are identified
by the serial numbers 495001, 496001, 497001, 498001 and 499001.
300
SOLUTION OF EXAMPLES
_-. . j. „ ±- n - rwp _j ,.4- f MT .« .>« f> 3 i>H taaA nnnirn} switch and restart calculator.
(4) Jttun starting tape. mien _a.ru» ±uu uui, nirn <_•_._. uiu _~_~ x._----. j — w_ — «--« _■>,« ... ,
,.. _. _i_.i_.___x . _-+-._ „,- _.-___>+._. tvi__ ..nuance TYiPfhanism will stoo on a blank line 01
u me starting tape 10 uumpicicu ^uiic^v-jij «."v, ^w^—^--^-
tape.
(5) If the check, on line 35 of the starting tape fails, the calculator will stop on line 36, reading
(7, 7, 7). The starting cards must be refed and the starting tape rerun. If the check continues
to fail, the counters used in the difference computation (ctrs. 1 through 15) and switch 8 must
be tested.
(6) Run main control tape. If no failures occur, continue running until the card for x,. = 9.99 has
been punched, then press the stop key.
(7) If it is necessary to rerun the computation, or to run it for an arbitrary value of the argu-
ment, x :
7 n
(a) five cards from those punched under control of the main tape must be placed in card feed I;
these cards are identified by the arguments Xj._ 5 , x n _ 4 , x 3 , x n _ 2 > x n -l' in that order '
punched in card columns 74-77 and a one in card column 80:
(b) switch 1 1 must be set to x n < ;
(c) the storting procedure must be repeated and the computation continued under control of the
main tape.
(8) The maximum time for each revolution of the main tape may be computed as follows:
computation of F(x n ) 12
punching F(x n ) 10
punching serial number _3
25 cycles = 7,5 seconds.
(9) The first card punched under control of the main sequence tape will be F(5.00) = 874.25 with
the serial number 500001 .
Plugging Instructions
(1) Plug the card punch as in example 1 (see page 296).
(2) Plug card feed I direct (see page 272).
Example 3. It is required to design a single control tape incorporating the two methods of evaluating
the polynomial, F(x), defined in example 1. The two values of F(x p ) independently computed in each
revolution of the tape are to be compared providing an exact check on the computation. All other
conditions of this example are the same as those of examples 1 and 2.
Starting Tape
Lines 1 through 35 will be lines 1 through 35 of the starting tape of example 2.
Lines 36 through 41 will be lines 1 through 6 of the starting tape of example 1.
SOLUTION OF EXAMPLES
301
Main Control Tape
ax to ctr. 1; ctr. 1 = x n _^ +ax = x n
ax to ctr. 64; ctr. 64 = x - +ax = x
ax to ctr. 2; ctr. 2 = x n + 3
x n + 3 to MC
x n to MP
- 0.75 to ctr. 3
(x n + 3)x n to ctr. 3
(x n + 3)^ - 0.75 to MC
F n _! to ctr. 12
aF o to ctr. 13
n-4
x to MP
n
a 2 F„ o to ctr. 14
n-o
a 3 F A to ctr. 15
n-4
- 22 to ctr. 4
((x n +3)x n - 0.75)x n to ctr. 4
((x + 3)x - 0.75)x - 22 to MC
n n n
A 4 F n _ 4 to ctr. 15; ctr. 15 = A 3 F n _ g
a 3 F to ctr. 14; ctr. 14 = a 2 F _
n-o n-^
x n to MP
a 2 F n to ctr. 13; ctr. 13 = a F ,
n-2 n-1
a F n _! to ctr. 12; ctr. 12 = F n
Rerun line
Line
OUT
IN
MISC.
1
741
1
7
2
742
7
7
3
741
2
7
4
2
761
7
5
43
43
7
6
431
431
7
1
7
8
432
432
7
9
4321
4321
7
10
21
21
7
11
7431
21
32
12
21
7
13
21
761
7
14
4
43
7
15
41
431
16
1
7
17
42
432
7
18
421
4321
7
19
3
3
7
20
7432
3
32
21
3
7
22
3
761
7
23
75
4321
7
24
4321
432
25
1
7
26
432 431
7
27
431 j 43
7
302
SOLUTION OF EXAMPLES
3 to ctr. 5
(((x n + 3)x n - 0.75)x n - 22)x n to ctr. 5; ctr. 5 = F
F to punch ctr.
n
F by multiplication to ctr. 6
- F„ by differences to ctr. 6
zero check tolerance to check ctr. 72
j-n *nj w w*^- w. *_-
check
initiate punching; continue operation, but complete punching
before reading into punch ctr.
F_ to ctr. 8
ii
aF i to ctr. 9
n-1
2
a F to ctr. 10
A 3 F „ to ctr. 11
n-o
Xjj for serial number to punch ctr.
1 in 1st machine column to punch ctr.
initiate minchins and continue one ration
Line
KJVi.
IN
MISC.
28
31
31
7
29
74321
31
30
31
7
31
31
753
32
32
32
7
33
31
32
7
34
43
32
732
35 [743
74
7
3fi !32
" I"
74
71
37 |74
74
64
38
4
4
751
39
41
41
7
40
42
42
7
41
421
421
7
42
43
4
43
1
431
41
7
44
432
42
7
45
4321
421
7
46
7
753
47
743
753
48
75
49
87
Operating Instructions
(1) Set switches as listed on page 293, adding switch 8 = 0.000 000 24. Punch the values set in the
switches and compare the punched values with the list of switch settings.
(2) The quantities punched under control of the main tape are the values of F^). Each card is to
be identified by a serial number consisting of the argument, x^, punched in card columns 74-77
303
SOLUTION OF EXAMPLES
and a one, the code for F(x), in card column 80. All cards punched are to be placed in the
drawer provided for this purpose.
(3) Five cards, labeled "starting cards", must be placed in card feed I. These cards are identified
by the serial numbers 495001, 496001, 497001, 498001 and 499001.
(4) Run starting tape. When cards run out, turn off card feed control switch and restart calculator.
If the starting tape is completed correctly, the sequence mechanism will stop on a blank line of
tape.
(5) If the check, on line 35 of the starting tape fails, the calculator will stop on line 36, reading
(7, 7, 7). The starting cards must be refed and the starting tape rerun. If the check continues
to fail, the counters used in the difference computation (ctrs. 1 through 15) and switch 8 must
be tested.
(6) Run main control tape. If no failures occur, continue running until the card for F(9.99) has
been punched, then press the stop key.
(7) If the check on line 37 of the main tape fails, the tape must be rolled back to line 4, marked
"Rerun line", and the computation repeated.
(8) If the check continues to fail, the computation should be re-established using the following pro-
cedure for Xj^:
(a) five cards from those punched under control of the main tape must be placed in card feed I;
these cards are identified by the arguments x n _ 5 , x^, x^g, x n _ 2 , x^, in that order,
punched in card columns 74-77 and a one in card column 80;
(b) switches 9, 10 and 11 must be set to the values indicated in the list on page 293;
(c) the starting procedure must be repeated and the computation continued under control of the
main tape .
(9) Repeated failure of the check under the roll back procedure of instruction (7) but correct oper-
ation under the procedure of instruction (8) probably indicates that the difference computation
is the source of error.
(10) If it is desired to run the computation for any arbitrary value of the argument, the procedure
of instruction (8) may be used.
(11) The maximum time for each revolution of the control tape may be computed as follows:
accumulate arguments 3
three multiplications 30
check procedure 6
punching F(x) 10
punching serial number _3
52 cycles = 15.6 seconds.
(12) The first card punched under control of the main sequence tape will be F(5.00) = 874.25 with
the serial number 500001.
Plugging Instructions
(1) Plug the multiply unit for the standard position of the operating decimal point (see page 247).
304
SOLUTION OF EXAMPLES
/<1\ D1..0 +U*v A n«v* rainnK no in ovamnla t /coo tV3CTCk 9Qfi\
\G) nug U1C waiu £»uift»u ■*.£> xu B^»«ii»i/iC ^ ^Sw^ £».*£,.*- »wv />
(3) Plug card feed I direct (see page 272).
Example 4 . It is required that the function,
U(x) = (x 2 - I)" 3 / 2 ,
be tabulated in the interval 5 £ x £ 10, with a x = 0.01, using an iterative process. It is further re-
quired that the values of U(x) be in error by less than 5 x 10" 10 and that the computation be completely
checked. The values of U(x) are to be punched in tabulating machine cards for use in further compu-
tation. Each card must be identified by a serial number consisting of the argument, x^ punched with
decimal point between card columns 75 and 76 (machine columns 5 and 6) and a two in card column 80
(2 in 1st machine column). It is not required to print the values of U(x). One value of U(x) is to be
computed during each revolution of the control tape. The tape is to be designed so that it may be
rolled back and rerun without any additional manipulations. The starting tape is to be designed so
that it may be used to re-establish the computation for any arbitrary value of the argument.
The value of Ufa) = U(x , ) = U , determined for the argument, x n 1 , will be used as the
n-i n-i n-i
first approximation to U(x n ) = U n . The value of U n will be obtained by the iterative formula,
4U n-l< N n + N n-l>
TT _
"n "
U n-l< N n + N n-1> 2 + 4N n
where x = x n _^ + ax ,
N n-1 - < X n-l " ^
N n Mx2-l)3
and U 2 = 1/N„ .
The error after one application of the iterative formula is
e l = e N n / 8 >
where e Q = U^ - U n .
It can be shown that one application of the iterative formula will give an error in U(x) of less than
2.7 x 10"**, slightly better than the accuracy required.
The computation of xj will be checked by use of the identity,
305
SOLUTION OF EXAMPLES
x 2 = x 2 , +2x .AX+AX 2
n n-1 n-1
The computation of N fl = (x 2 - l) 3 will be checked by comparing it with the value of
".-(^-sj^+W^-i.
The quantities U n N n and N n U n will be computed and compared with each other. Finally, the value of
U n will be checked by means of the identity,
The operating decimal point will be assumed to lie between columns 15 and 16 and division will be
plugged for 14 comparisons. The switch settings required by the starting tape and the main control
tape are given in the following table.
Switch Settings
No.
1
2
4
7
9
11
12
13
14
15
16
Code
741
742
743
74321
751
7521
753
7531
7532
75321
754
Setting and Purpose
a x = 1 in 14th machine column; increment of argument for computing
ax = 1 in 4th machine column; increment of argument for punch card serial
numbers
1 in 1st machine column; zero check tolerance
x n _l = argument for computing; decimal point between columns 15 and 16;
used in starting tape only
x n-l = argument for punch card serial numbers; decimal point between col-
umns 5 and 6; used in starting tape only
——2
ax' = 1 in 12th machine column
2 in 1st machine column; code for U(x)
X n-2 AX = x n-2 ^h decimal point between columns 13 and 14; used in start-
ing tape only
6 in 8th machine column; tolerance on check of U_
Starting Tape
x , to MC
n-1
Line
OUT
IN
MISC.
1
751
761
7
2
1
1
7
306
SOLUTION OF EXAMPLES
x . to ctr. 1
n-1
*n-l
to MP
- 1 to ctr. 18
x n-l to ctr * ^
x2_ x to ctr. 18; ctr, 18 = xj_j - 1
(xf , - 1) to MC
U-JL
x n-l to ctr * ^
k?-l " 1} to MP
x 2 AX ^° ctr « *^
(x n-l " l)2 to ctr> 19
(xl_ x - l) 2 to MC
< x n-l ~ X > t0 MP
(xf 1 - l) 3 to ctr. 20; ctr. 20 = N n _ t
U„ * to ctr. 25 from card feed I
n-i
Line
OUT
IN
MISC.
3
751
1
4
751
7
5
7
7
7
6
52
52
7
7
75321
52
732
8
5
5
9
5
7
10
5
52
7
11
52
761
7
12
74
74
7
13
7521
7
14
52
7
15
51
51
7
18 j
7532
51
•7 i
i j
17 !
7 !
1
!
18
521
521
!
19 I
521
7
20
521
761
7
21 j
i
22
1
1
23
52
7
24
7
25
7
26
541
541
7
27
53
53
28
53
7
29
541
7632
SOLUTION OF EXAMPLES
307
U n-1 to MC
N n _ t to MP
U n-l N n-l to ctr » 26
Line
OUT
IN
MISC.
30
541
761
7
31
7
32
33
53
7
34
7
35
7
36
7
37
542
542
38
542
7
Main Control Tape
ax to ctr. 1; ctr. l=x , + ax = x
n-i n
ax to ctr. 64; ctr. 64 = x„ , + ax = x
n-i n
ax 2 to ctr. 17; ctr. 17 = ^ax + ax 2 = x ax
x n to MC
x n , to ctr. 4
n-l
x to MP
n
x n _jAx to ctr. 4
- 1 to ctr. 18
x n to ctr. 3
x 2 to ctr. 18
(x 2 - 1) to MC
x^jAx to ctr. 4
ax 2 to ctr. 4; ctr. 4 = x 2
Rerun line
1
741
1
7
2
742
7
7
3
753
51
7
4
1
761
7
5
3
3-
7
6
5
3
7
1
7
8
51
3
7
9
52
52
7
10
75321
52
732
11
21
21
12
21
7
13
21
52
7
14
52
761
7
15
51
3
7
16
753
3
308
SOLUTION OF EXAMPLES
(x n ' X) t0 MP
x fl to ctr. 6
- x^ to ctr. 6
(x 2 - l) 2 to ctr. 19
zero check tolerance to check ctr. 72
(x 2 - 1) to MP
- 3 to ctr. 21
x 2 to ctr. 21
n
(JZ _ -n3 tn ctr 20: ctr. 20 = N_
v- n -,--■•- -
(x? - 3) to MC
x£ to MP
3 to ctr. 22
_ t J2 = ^2 | + c h ec k ctr.- 72
I A n "n I
check
(x 2 - 3)x 2 to ctr. 22
(x 2 - 3)x 2 + 3 to MC
SOLUTION OF EXAMPLES
309
x£ to MP
- 1 to ctr. 23
((xj* - 3)xj* + 3)x^ to ctr. 23; ctr. 23 = N
U ! toMC
n-i
U n1 N n1 to ctr. 27
n-i n-l
N to MP
n
N to ctr. 4
n
N to ctr. 4
N to ctr. 4
U ,N to ctr. 27
n-l n
U .(N +N J toMC
n-l v n n-l'
N to ctr. 4; ctr. 4 = 4N
n n
U„ i(N+N„ J to MP
n-l n n-l
U„ i(N„ + N t ) to ctr. 5
n-l n n-l
U„ i(N„ +N„ «) to ctr. 5
n-l n n-l
u r, i( N « + N n 1) to ctr. 5
n-l n n-l
U n-l( N n + N n-l) to ctr « 5 ' ctr - 5 = 4U n-l( N n + N n-l)
U n-l( N n + N n-l) 2toctr ' 4
U nV N n + N n-l) 2+4N n toDR
Line
OUT
IN
MISC.
44
21
7
45
7
46
7
47
5321
5321
7
48
75321
5321
32
49
5321
7
50
541
761
7
51
5421
5421
7
52
542
5421
53
53
7
54
3
3
7
55
53
3
7
56
53
3
7
57
53
3
58
5421
7
59
5421
761
7
60
53
3
7
61
31
31
62
5421
7
63
5421
31
7
64
5421
31
7
65
5421
31
7
66
5421
31
67
3
7
68
3
76
7
69
321
321
7
70
310
SOLUTION OF EXAMPLES
4U JN +N J toDD
n-1 n n-1
N to ctr. 6
n
- N to ctr. 6
n
zero check toJerance to check ctr. 72
- N - N to check ctr. 72
In nl
check
U to ctr. 7
n
U toMC
n
N to MP
n
U N to ctr. 12
n n
N toMC
n
Line
OUT
IN
MISC S
71
31
?
72
7
. 73
7
74
7
75
7
76
7
77
7
78
7
79
32
32
7
80
53
32
7
81
5321
32
732
82
743
74
7
83
32
74
71
84
74
74
64
85
!321
!
86
321
7
87
321
761
7
88
7
89
90
53
7
91
7
92
7
93
7
94
43
43
95
43
7
96
53
761
7
97
7
SOLUTION OF EXAMPLES
311
U to MP
n
- 1 to ctr. 14
U N to ctr. 6
n n
N U to ctr. 13
n n
U toMC
n
-N U to ctr. 6
n n
zero check tolerance to check ctr. 72
UN to MP
n n
- | UN -NUl to check ctr. 72
n n n n
check
U^N n to ctr. 14; ctr. 14 = U^N n -1
tolerance on U to check ctr. 72
-|U^N n - 1 I to check ctr. 72
check
U to punch ctr.
initiate punching
x to ctr. 16
n
U to ctr. 25
n
U n N n to ctr. 26
x for serial number to punch ctr,
n
Line
OUT
IN
MISC.
98
432
432
99
321
7
100
75321
432
732
101
32
32
7
102
43
32
7
103
431
431
104
431
7
105
321
761
7
106
431
32
732
107
743
74
108
43
7
109
7
110
32
74
71
111
74
74
64
112
432
113
432
7
114
754
74
7
115
432
74
71
116
74
74
64
117
321
753
118
5
5
751
119
21
5
7
120
541
541
7
121
321
541
7
122
542
542
7
123
43
542
124
7
753
i
312
SOLUTION OF EXAMPLES
Line
OUT
IN
MISC,
125
7531
753
126
75
127
87
2 in 1st machine column to punch ctr.; code for U(x)
initiate punching and continue operation
Operating Instructions
(1) Set switches as listed on page 305. Punch the values set in the switches and compare the punched
values with the list of switch settings.
(2) The quantities punched under control of the main tape are the values of U(x ). Each card is
identified by a serial number consisting of the argument, x , punched in card columns 74-77
and a two, the code for U(x), in card column 80. All cards punched are to be placed in the
(3) One card labeled, "starting card", followed by a blank card, must be placed in card feed I. This
card is identified by the serial number 499002.
(4) Run starting tape. When cards run out, turn off card feed control switch and restart calculator.
When the starting tape is completed, the sequence mechanism will stop on a blank line of tape.
(5) Run main control tape. If no failures occur, continue running until the card for U(9.99) has
been punched, then press stop key.
(6) If any of the checks in the main tape fail, the tape must be rolled back to line 4, marked "Rerun
line", and the computation repeated.
(7) The following checks are included in the main control tape.
Lines
24, 37-38
82-84
107, 110-111
114-116
Quantity Checked
2 -2
xjj - xjj from ctr. 6
N n - N n from ctr. 6
TT M . V I] fx^™ «,+„ a
Uj|N n - 1 from ctr. 14
Tolerance
1 in 1st machine column from sw. 4
1 in 1st machine column from sw. 4
1 in 1st machine column from sw. 4
6 in 8th machine column from sw. 16
(8) If a check repeatedly fails, the quantities involved in the computation being checked should be
punched in cards, and manual computations used to assist in tracing the source of error.
(9) If it is desired to run the computation for any arbitrary value of the argument, x , or to re-
establish operation after tests have been made and counters disturbed, the following steps must
be taken:
(a) a card from those punched under control of the main tape, followed by a blank card must be
placed in card feed I; this card is identified by the argument, x^ i , punched in card col-
umns 74-77 and a two in card column 80; care must be taken to replace this card properly
after it is used;
313
SOLUTION OF EXAMPLES
(b) switches 9, 11 and 14 must be set to the values indicated in the switch list on page 305;
(c; the starting procedure must be repeated and the computation continued under control of the
main tape.
(10) The maximum time for each revolution of the control tape may be computed as follows:
accumulate arguments 3
additions 5
multiplication by x n io
4 multiplications by xg and x£ - 1 48
2 multiplications by N n 36
multiplication by U n 15
multiplication by IV^Nn + N n _ 1 ) 18
division to 14 comparisons 34
multiplication by U n N n 18
punching U(x) 10
punching serial number 3
200 cycles = 60 seconds.
Plugging Instructions
(1) Plug the multiply unit for the standard position of the operating decimal point (see page 247).
(2) Plug the divide unit for 14 comparisons using the blank code as shown in the following diagram.
MP-DIV PLUGBOARD
Row 1 Aoooo 00000 0*000 00000 00000
25 20 15 10 5
Set divide switch to 07.
(3) Plug the card punch as in example 1 (see page 296).
(4) Plug card feed I direct (see page 272).
Example 5. The output cards containing F(x) and U(x) as obtained in examples 3 and 4 are to be fed
to the calculator to form the function,
f(x) = F(x) • U(x) .
It is required that a two column table be printed consisting of the argument, x n , followed by the
values of f(x n ). The values of f(x fl ) are to be printed to six decimal places, the digits being grouped
by threes to the right and left of the decimal point. The lines of the table are to be spaced in vertical
groups of five lines. The quantities F(x) . U(x) and U(x) . F(x) are to be computed and compared
with each other. The print counter read-out is to be checked. It will not be required to punch the
values of f(x) in tabulating machine cards. This could be done, however, without loss of time.
314
SOLUTION OF EXAMPLES
x i to ctr. 1
n-l
Line
OUT
IN
MISC.
1
1
1
7
2
751
1
7
Main Control Tape
ax to ctr. 1; ctr. 1 = x^j + ax = x n
x n to print ctr . I
initiate printing
F(x) to ctr. 35 from card feed I
U(x) to ctr. 36 from card feed II
F(x) to MC
U(x) to MP
zero check tolerance to check ctr . 72
f(x) = F(x)U(x) to ctr. 37
U(x) to MC
reset print ctr. I
F(x) to MP
f(x) to print ctr. I
f(x) from print ctr. I to ctr. 39
- f(x) from ctr. 37 to ctr. 39
Rerun line
1
741
1
2
1
7432
3
87
752
76
4
621
I
621
7
5
63
63
7
6
621
7632
7
1 ,
63
76321
8
|621
761
7
9
631
631
7
10
j 632
632
11
1 .
7
12
6321
6321
7
13
1 74
74
7
14
743
74
7
15
64
64
16
1 1
\i
631
I 1
l
17
63
761
7
18
842
7
19
20
621
7
21
631
7432
22
862
6321
7
23
631
6321
732
SOLUTION OF EXAMPLES
315
f(x)toctr.40
- |f(x) - f(x) | to check ctr. 72
check of print ctr. I read-out
f(x) = U(x)F(x) to ctr. 38
zero check tolerance to check ctr. 72
-f(x) to ctr. 40
-|f(x) - f(x) I to check ctr. 72
check multiplication
initiate printing
Line
OUT
IN
MISC.
24
631
64
7
25
6321
74
71
26
74
74
64
27
632
28
632
7
29
743
74
7
30
632
64
732
31
64
74
71
32
74
74
64
33
752
76
34
87
Operating Instructions
(1) Set switches as listed. Punch the values set in the switches and compare the punched values
with the list of switch settings . . ' ■
Switch Settings
No.
Code
Setting and Purpose
1
4
9
741
743
751
a x = 1 in 14th machine column; increment of argument for printing
1 in 1st machine column; zero check tolerance
x - = argument for printing; decimal point between columns 15 and 16;
used in starting tape only
(2) Card feed I must contain the cards for F(x), identified by the code 1 in the 80th card column.
Card feed n must contain the cards for U(x), identified by the code 2 in the 80th card column.
Care must be taken that the cards in each feed contain identical serial numbers in card col-
umns 74-77. One card is fed from each feed during each revolution of the control tape. The
first cards fed must contain the serial numbers 500001 and 500002 for card feeds I and II,
respectively.
(3) Run starting tape. When the starting tape is completed, the sequence mechanism will stand on
a blank line of tape.
(4) Start main control tape. The sequence mechanism will stop on line 2. Press start key and con-
tinue operation. If no failures occur, continue running until the argument 10.00 has been print-
ed, then press stop key.
316
SOLUTION OF EXAMPLES
^5^ If the check on line ^6 fails, the print counter read-out Suoulu v& tested, u. %-h.q storage counvers
___ 4. j;_t.._1 1 4-U« 4-~~„ « nn tU„_ V»« _.-v11„J Un/>lr 4-n Knn O r> vis] tli/i nnmnntotinn rvonoltoH
<UC 11UI UlDlUi UCU, tMC LttjJC XlldJT UiGll UC 1 UilCU UO.V.IV lu liuc u atiu uic buiu^/uuiuuii j. \^£>v,u.wx» .
(6) If the check on line 32 fails, the multiply unit should be tested. If the storage counters are not
disturbed, the tape may then be rolled back to line 8 and the computation repeated.
(7) If storage counters have been disturbed by testing, the computation must be re-established
using the following procedure for the argument, x n :
(a) card feed I must contain the cards for F(x), (code 1 in the 80th card column), the first
card containing the serial number Xj, in card columns 74-77;
(b) card feed II must contain the cards for U(x), (code 2 in the 80th card column), the first
card containing the serial number x in card columns 74-77;
(c) switch 9 must be set to x _, , the value indicated in the switch list;
(d) the starting procedure must be repeated and the computation continued under control of the
main tape;
(e) the typewriter vertical spacing must be checked and properly reset,
(8) The maximum time for each revolution of the control tape may be computed as follows:
print argument 14
multiplication by U(x) 15
check f(x) 4
print f(x) 14
47 cycles = 14.1 seconds.
Plugging Instructions
(1) Plug the multiply unit for the standard position of the operating decimal point (see page 247).
(2) Plug the card feeds direct (see page 272).
(3) Plug typewriter I as shown in the diagram below.
DP TAB FUNCTIONAL PLUGBOARD
Row 1 * o o o o o •— •— • ^~
R TAB _
Row 2 • o o o k
xvuw o u u u u u
• * O O O
'20
20
Row 4 o • 4 • »
24
C
Row 5 •— • ooo ooo
2524 20
SPACES
5 I I rio
ooo
25
15
/
30
U \J u
J
40
Li. j:
is r
35
o o
\J \J \J VJ \J \J
45
-•OOOO 0000
10 5
O OOOOO 00000 00000
15 10 5
Row 6 • o o o o ooooo ooooo ooooo ooooo
2524 20 15 10 5
Row 18 ooooo ooooo ooooo ooooo o o o o •-
2 1
TYPEWRITER I
COL-SEL
PRINT CTR RO
RO-RELS
317
SOLUTION OF EXAMPLES
FUNCTIONAL PLUGBOARD
Row 38 ooooo ooooo ooooo oooo* ooooo
98765 4321 10 98765
4 3 2 1 10
Row 39 ooooo ooooo ooooo oooot ooooo
R R
Example 6. It is required that a single main control tape be designed to compute,
f(x) = F(x) . U(x),
as defined in example 5. It is further required that the values of f(x) be in error by less than 5xl0~l*
and that the computation be completely checked. The values of f(x) are to be punched in tabulating
machine cards for use in further computation. Each card must be identified by a serial number con-
sisting of the argument, x R , punched with decimal point between card columns 75 and 76 and a three
in the 80th card column. It is not required to print the values of f(x). One value of f(x) is to be com-
puted during each revolution of the control tape. The tape is to be designed so that it may be rolled
back and rerun without any additional manipulations. The starting tape is to be designed so that it
may be used to re-establish operation for any arbitrary value of the argument.
Since F(x)< 2 x 10 , U(x) must be in error by less than 2.5 x 10" , in order that f(x) be cor-
rect to the required accuracy. Two applications of the iterative process will be necessary to provide
the desired accuracy in U(x) .
In order to provide for rerunning and re-establishing the computation, it will be necessary to
punch cards containing F(x) and U(x) during each revolution of the tape. Thus the main control tape
will combine the tapes of examples 3, 4 and 5. The starting tape will combine the essential features
of the starting tapes of these examples. The interweaving of the coding of these tapes is left as a
problem for the reader.
The computation as performed by the three separate tapes would require:
computation of F(x) 15.6
computation of U(x)
(including two iterations) 86.4
computation of f (x) 14.1
116.1 seconds .
The computation as performed by a single control tape should not require more than 98 seconds.
318
SOLUTION OF EXAMPLES
Example 7, JjCT it De assumed thai ine iuncuuu, i\a; vwenncu in cAauijuc «/, new tree** wm^-l^u » —
an error of less than 4 x 10" 10 , over the interval 4.99 sxs 10.02, with ax = 0.01, and punched in
tabulating machine cards. The cards have been punched with serial numbers, equal to x n with deci-
mal point between card columns 22 and 23. It is now required to compute, check and print the values
of the integral, /* x n
I(x)=v£ f(x)dx,
over the interval 5<xsl0. It is further required that a two column table be printed consisting of
the argument, x n , followed by the values of I(x n ). The lines of the table are to be spaced in vertical
groups of five lines.
The approximate quadrature formulae,
Al =/"" f(x)dx = (-f n-1 + 8f n + 5f n+1 )Ax/12 + R,
'Si-i
a! =£* n ffaOdx = (5f n + 8f n+1 - f n+2 ) ax/12 - R,
n-1 .
where R =ax i \ \ )/™*s
in the interval 4.99 £ £ s 10.02, may be used since for the given f(x), R < 6.66 x 10" . Hence the
error in the integral 1(10) wUl be less than 3.4 x 10" 8 . The values of I(x) will be printed to eight
decimal places, with a half-correction in the ninth place, making the tabular values in error by less
than 4 x 10" 8 . The digits will be grouped by fours to the right and left of the decimal point. Each
revolution of the main control tape will compute and compare the quantities a I and a! . The values
of a I will be used to accumulate the values of I(x). The serial numbers of the cards supplying f(x)
will be checked. The print counter read-out and the half-correction will be checked before the tabular
values are printed on typewriter II . Typewriter I will print the argument, the value of the integral
__j +v~ J4«~„„r,„ a t _ H KofnT-e thp checks are comdeted in order to provide information in case
of machine failure. In order to provide for rerunning and re-establishing the computation, if neces-
sary, the values of I(x) will be punched in tabulating machine cards. The values set in the switches
are listed under the operating instructions.
Starting Tape
x^ 1 to ctr. 1
Line
OUT
IN
MISC.
i
1
1
7
2
751
1
7
SOLUTION OF EXAMPLES
319
f t + x to ctr. 2 from card feed I
n-1 n-1
f n 1 +x„ ! to SIO ctr.
n-i n-i
f . to ctr. 16
n-i
x n-l to ctr# 3
x„ , to ctr. 64
n-l
- x„ 1 to ctr. 3
—n-1
zero check tolerance to check ctr. 72
" *n-l + -n-1 to cneck ctr « ? 2
check
f n + x n to ctr. 2 from card feed I
f n + x n to SIO ctr.
f n to ctr. 17
x to ctr. 3
n
- x 1 to ctr. 3
-n-1
- 1 in 1st machine column to ctr. 3
zero check tolerance to check ctr. 72
- x n - x nl - 1 to check ctr. 72
check
f n to MC
Line
OUT
IN
MISC.
3
2
2
7321
4
2
7632
5
2
874
7
6
5
5
7
7
874
5
7
8
21
21
7
9
84
21
7
10
7
7
7
11
7521
7
7
12
7
21
732
13
74
74
7
14 J 743
74
7
15 121
74
71
16 174
74
64
17
2
2
7321
18
2
7632
19
2
874
7
20
51
51
7
21
874
51
7
22
21
j
21
7
23
84 |21
1
7
24
7
i ■
21 !732
I
25
743
21
732
26
743
74
7
27
21
74
71
28
74
74
64
29
51
761
7
320
SOLUTION OF EXAMPLES
f to ctr. 5
n
5 to MP
f to ctr. 5; ctr. 5 = 2f „
n n
f to ctr. 5; ctr. 5 = 3f
n n
f to ctr. 5; ctr. 5 = 4f R
5f to ctr. 4
n
f to ctr. 5; ctr. 5 = 5f
n n
5f to ctr. 6
n
- 5f to ctr. 6
n
zero check tolerance to check ctr. 72
of - 5f to check ctr. 72
n n I
check
5f to ctr. 18
n
f toMC
n
f to ctr. 5; ctr. 5 = 6f_
n n
f n to ctr. 5; ctr. 5 = 7f n
8 to MP
f n to ctr. 5; ctr. 5 = 8f n
8f to ctr. 6
n
8f to ctr. 4
n
- 8f to ctr. 6
n
Line
OUT
IN
MISC. |
30
31
31
7
31
51
31
32
7541
7
33
51
31
7
34
51
31
7
35
51
31
7
36
3
3
37
3
7
38
51
31
7
39
32
32
7
40
31
32
7
41
3
32
732
42
743
74
7
43
32
74
7i
44
74
74
64
45
52
52
7
46
3
52
7
47
51
761
7
48
1 c«
01
n
49
| 51
1
31
50
17542
7
51
51
31
7
52
32
32
7
53
I 31
32
7
54
3
3
55
3
7
56
3
32
732
321
SOLUTION OF EXAMPLES
zero check tolerance to check ctr. 72
- I 8f n - 8f n I to check ctr. 72
check
8f n to ctr. 19
f n+1 + x - to ctr. 2 from card feed I
f i + x i to SIO counter
n+1 n+1
f n+1 to ctr. 20
x to ctr. 3
n+1
- X. , to ctr. 3
— n-i
- 1 in 1st machine column to ctr. 3
- 1 in 1st machine column to ctr. 3
zero check tolerance to check ctr. 72
-x 1 -x , -1-1 to check ctr. 72
I n+i —n-i |
check
ICx^j) + x^j to ctr. 2 from card feed II
^n-l^ + *n-l to S ^ counter
Kx^j) to ctr. 21
x\ 1 to ctr. 3
n-i
- x„ , to ctr. 3
— n-i
zero check tolerance to check ctr. 72
Line
OUT
IN
MISC.
57
743
74
7
58
32
74
71
59
74
74
64
60
521
521
7
61
3
521
7
62
2
2
7321
63
2
7632
64
2
874
7
65
53
53
7
66
874
53
7
67
21
21
7
68
84
21
7
69
7
21
732
70
743
21
732
71
743
21
732
72
743
74
7
73
21
74
71
74
74
74
64
75
2
2
7321
76
2
76321
77
2
874
7 1
78
531
531
7 1
79
874
531
7
80
21
21
7
81
84
21
7
82
7
21
732
83
743
74
7
322
SOLUTION OF EXAMPLES
- i x . - x « to check ctr. 72
n-1 -n-1 1
check
- x , to ctr. 2
n-1
x « to LIO ctr.
-n-1
x - to ctr. 2
-n-1
zero check tolerance to check ctr. 72
- - x * + x -to check ctr . 72
I n-1 -n-1 I
check
Main Control Tape
ax to ctr. 1; ctr. 1 = x^ + ax = x n
x„ to print ctr. I
n
print with argument control
f n+ 2 + x_ + 2 to ctr. 15 from card feed I
f n+1 toMC
- f - to ctr. 6
n-i
5 to MP
8f„ to ctr. 6
n
Rerun line I
Rerun line II
5f . to ctr. 4
n+i
x to print ctr. II
Line 1
OUT
IN
MISC.
34
21
74
71
85
74
74
64
86
2
2
763
87
1
2
732
88
7
765421
7
89
831
2
7
90
743
74
7
91
2
74
71
92
74
74
64
93
7
1
741
1
7
2
1
1
7432
3 !
87
752
76 j
4
4321
4321
I !
7
5
4321
7632
6
53
761
7
7
32
32
7
8
5
32
32
9
7541
7
10
521
32
7
11
432
432
7
12
321
321
7
13
3
3
14
3
15
1
74321
SOLUTION OF EXAMPLES
323
print with argument control
f n+1 to MC
5f n+1 to ctr. 6
5f n to ctr. 7
8 to MP
f n+2 +5E n + 2 ^ SIO ctr.
f n+2 toctr.3
8f 1 to ctr. 5
n+1
- 1 in 1st machine column to ctr. 14
( - *n-l + 8f n + 5 W to M ^
8f n+1 toctr.7
- f n + 2 t0 ctr - 7
ax/12 to MP
- 1 in 1st machine column to ctr. 14
*n+2 to ctr - 14
ax to ctr. 64; ctr. 64 = x^ + ax = x^
- x fl to ctr. 14
zero check tolerance to check ctr. 72
I(x n j) to ctr. 11
Al(x n ) to ctr. 8
Al(x ) to ctr. 11; ctr. 11 = I(x )
I(x n ) to print ctr. I
Line
OUT
IN
MISC.
16
87
7521
7
17
53
761
7
18
3
32
7
19
52
321
20
7542
7321
21
4321
874
7
22
21
21
7
23
874
21
7
24
31
31
25
31
7
26
743
432
732
27
32
761
7
28
31
321
7
29
21
321
32
30
75421
7
31
743
432
732
32
84
432
7
33
742
7
7
34
7
432
732
35
743
74
7
36
421
421
7
37
531
421
7
38
4
4
39
4
7
40
4
421
7
41 :
421
7432
42 j
752
76
=-. r-
324
SOLUTION OF EXAMPLES
< 5f n + 8f n + l " W to MC
ax/12 to MP
I(x ) to ctr. 12
n-1
I6c ) to ctr. 13
v n'
- I x „ - x - 1 - 1 I to check ctr. 72
I n+2 -n I
check
a! to ctr. 9
- a! to ctr. 10
a T - a I to print ctr. I
print
tolerance on a I to check ctr. 72
- a I - a! to check ctr. 72
check
a! to ctr. 12; ctr. 12 = I(xJ
I(x ) to ctr. 2
n
- 1^) to ctr. 2
tolerance on a I to check ctr. 72
- 1 I(x n ) - IfxJ I to check ctr. 72
check
Line uui
IN
MISC.
43 || 321
761
7
44 1 41
41
7
45 || 43
43
46 75421
7
47 || 531
43
7
48 (J 431
431
7
49 || 421
431
7
50 |4>
42
7
51 4
42
7
52
432
74
71
53
74
74
64
54
41
55
41
7
1
56
41
42
32
57
42
7432
58
752
7
59
7543
74
!
7
60
42
74
71
61
74
74
64
62
41
43
7
63
2
2
7
64
421
2
7
65
43
2
732
66
7543
74
7
67
2
74
71
68
74
74
64
69
5
5
7
SOLUTION OF EXAMPLES
325
f to ctr. 16
n
f , to ctr. 17
n+1
5f n+1 to ctr. 18
8f n+l t0 ctr * 19
f +2 to ctr. 20
I(x n ) to ctr. 21
reset print ctr. II
I(x n ) to print ctr. II
half -correction to print ctr . II
I(x ) + half -correction to ctr. 2
- half -correction to ctr . 2
- I(x ) to ctr. 2
n
zero check tolerance to check ctr. 72
- | I(x ) + half -correction - half-correction - I(x_) | to check
ctr. 72 ^
check
print
I(x n ) to SIO ctr.
x to ctr. 3
I(x n ) to ctr. 3
I(x ) +x to punch ctr.
n n
Line
OUT
IN
MISC.
70
51
5
7
71
51
51
7
72
53
51
7
73
52
52
7
74
3
52
7
75
521
521
7
76
31
521
7
77
53
53
7
78
21
53
7
79
531
531
7
80
421
531
7
81
8421
7
82
421
74321
83
75431
74321
84
2
2
7
85
8621
2
7
86
75431
2
732
87
421
2
732
88
743
74
7
89
2
74
71
90
74
74
64
91
7521
76
92
21
21
7321
93
421
874
7
94
7
21
7
95
874
21
7
96
21
753
326
SOLUTION OF EXAMPLES
punch
1 in 1st machine column to ctr. 71
tolerance for end of page stop to check ctr. 72
- number of lines to check ctr. 72
check
Line
OUT
IN
MISC.
97
5
98
743
7321
7
99
7421
74
7
100
7321
74
71
101
74
74
64
102
7
103
i i
87
Operating Instructions
(1) Set switches as listed in the following table. The operating decimal point lies between columns
16 and 17. Punch the values set in the switches and compare the punched values with the list of
switch settings.
Switch Settings
No.
Code
Setting and Purpose
1
741
ax = 1 in 15th machine column; increment of argument for printing
2
742
ax = 1 in 1st machine column; increment of argument for punch card serial
numbers
3
7421
5 in 2nd machine column
4
743
1 in 1st machine column; zero check tolerance
9
751
x nl = argument for printing; decimal point between columns 16 and 17; used
in starting tape only
11
7521
x j = argument for punch card serial numbers; decimal point between col-
umns 2 and 3: used in startincr tane onlv
17
7541
5
18
7542
8
19
75421
0.0008 3333 3333 = a x/12
20
7543
tolerance on check of a I; 1 in 7th machine column, 4 in 6th machine column
21
75431
5 in 8th machine column; half-correction
327
SOLUTION OF EXAMPLES
(2) The "85-1 P.U." switch and the "SIO-OUT-2 Invert Control" switch must be in the off position
before running any part of this computation, (see page 139).
(3) The values punched under control of the main tape are the values of I(x ). Each card is identi-
fied by a serial number, x n , punched with decimal point between card columns 22 and 23. All
cards punched are to be placed in the drawer provided for this purpose.
(4) Card feed I must contain the cards for f(x). When starting, the first card fed must contain the
serial number 0499 in card columns 1-4. When rerunning for the argument, x n , the first card
fed must contain the serial number, x-.j, in card columns 1-4. Three cards are fed under con-
trol of the starting tape, and one card during each revolution of the main tape. The card fed
during the revolution of the control tape for x n has the serial number x n+2 .
(5) Card feedn is used only when starting and rerunning. When starting the computation, card feed
II must contain a starting card and a blank card. When rerunning for the argument, x n , the
card with serial number x n _x, previously punched by the main control tape, followed by a blank
card must be placed in card feed n. Care must be taken to replace this card properly after it
is used.
(6) Run starting tape. When cards run out in card feed II, turn off card feed control switch and
restart calculator. When the starting tape is completed correctly, the sequence mechanism will
stop on a blank line of tape.
(7) The checks in the starting tape are listed in the following table.
Lines
Quantity Checked
Tolerance
14-16
serial number of 1st card from feed I
1 in 1st machine column from switch 4
26-28
serial number of 2nd card from feed I
1 in 1st machine column from switch 4
42-44
5f n computed by multiplication and by
addition
1 in 1st machine column from switch 4
57-59
8f computed by multiplication and by
addition
1 in 1st machine column from switch 4
72-74
serial number of 3rd card from feed I
1 in 1st machine column from switch 4
83-85
serial number of card from feed II
1 in 1st machine column from switch 4
90-92
argument for printing
1 in 1st machine column from switch 4
(8) If the sequence mechanism stops on lines 17, 29, or 75 of the starting tape, the wrong cards
have been fed from card feed I, and the starting tape should be rerun, with the cards corrected.
(9) If the sequence mechanism stops on line 86 of the starting tape, the wrong card has been fed
from card feed II, and the starting tape should be rerun, with the cards corrected.
(10) If the sequence mechanism stops on line 45 or 60 of the starting tape, the failure is probably in
the multiply unit or in counter 5. The starting tape must be rerun with the cards replaced in
both feeds.
328
SOLUTION OF EXAMPLES
,,.,.» _. ,, ^. .« --».«..*<? *, o — +»-© -jiAfk ™r, n«o 05 r>f thp starting tane (blank, blank, 7),
(11) if the sequence mechanism stops uu «.«e CiecK uu ^ ~~ — lfllwu -» . * , * • - .. _
v '■ ..., _ « ___ ^ 4 i __j 4. 1 o ra n „^ cm ohrmiH hp tpstpd since this check compares the
swucnes » a.nu n <uiu tumucio a, *<, w^ <ui« ~*~ -**
argument for printing with the argument for the punch card seriai numbers.
(12) Run main control tape until the "end of page stop" check stops the machine after 50 lines have
been printed. Reset counter 71, start new page on typewriter II and space up typewriter I. if
no failures occur, continue running until cards run out in card feed I, turn off card feed control
switch, restart calculator and press stop key.
(13) The checks in the main control tape are listed in the following table. ^____
Lines
35, 52-53
59-61
68-68
88-90
Quantity Checked
serial number of card feed I
a I computed two ways
print counter II read-out and half- correction
Tolerance
1 in 1st machine column from switch 4
i in 7th machine column, 4 in 6th ma=
chine column from switch 20
1 in 7th machine column, 4 in 6th ma-
chine column from switch 20
1 in 1st machine column from switch 4
(14) If the sequence mechanism stops on line 54 of the main control tape, while computing for the
argument, x , the wrong card has been fed from card feed I. The cards in card feed I must be
checked and replaced, the card with serial number x^ +2 being the first card fed. The main con-
trol tape must be rolled back to line 4, marked "Rerun line I", and the computation repeated.
Typewriter I must be spaced up, and its vertical spacing checked as the computation proceeds.
(15) If the sequence mechanism stops on line 62 of the main control tape, the tape mus^be rolled
back to line 6, marked "Rerun line II Tr , and the computation repeated, ^ewruer . mus. „e
spaced up, and its vertical spacing checked as the computation proceeds Typewriter II must be
turned off and kept off until after that line in the tape (line 30) at which the argument has fin-
ished printing. It must then be turned on in order to print the correct value of the function.
(16) If the sequence mechanism stops on line 69 of the main control tape, the addition of a I to I has
failed, and the counters involved should be tested. If the quantities in the counters are not dis-
turbed', the tape may be rolled back and rerun as in instruction (15).
(17) If the sequence mechanism stops on line 91 of the main control tape, either the print counter
read-out or tne nan-correcuon uaa iancu, <wu mc ^uvmvcx^ •.«»«*»»-». ~. ~~ .
quantities in the counters are not disturbed, the tape may be rolled back and rerun as in in-
struction (15).
(18) If counters are disturbed in testing and it is necessary to re-establish the computation for the
argument, x n , the following procedure must be carried out:
(a)
(b)
(c)
(d)
switches 9 and 11 must be set to x x as indicated in the switch list on page 326;
card feed I must contain the cards for f(x), the first card containing the serial number x n-1 ;
card feed II must contain the card with serial number x n-1 , from among those previously
punched by the main control tape, followed by a blank card; care must be taken to replace
the functional card oroDerly after it is used;
run the starting tape; when the cards run out in card feed II turn off card feed control switch
and restart calculator;
329
SOLUTION OF EXAMPLES
(e) run the main control tape starting on the "start line", and continue the computation;
(f ) typewriter I must be spaced up and its spacing checked as the computation is continued;
(g) typewriter II must be turned off and kept off until just before the correct function is printed.
(19) The maximum time for one revolution of the main control tape may be computed as follows:
3 prints on typewriter I 48
2 prints on typewriter II 28
cycles not covered by printing ljJ
88 cycles = 26.4 seconds.
Plugging Instructions
(1) The multiply unit must be plugged for operating decimal point between columns 16 and 17, with
the plugging to the four lowest columns of the buss omitted as shown in the following diagram .
Row 2
25
MP-DIV PLUGBOARD
ooooo ooooo ooooo ooooo PQ CTR
20 15 10 5
Row 3 ofooo ooooo o<
46 45 40
Row 4 o
35
30
PQCTR
oooo P-OUT
24
20
15
10
(2) The LIO counter must be plugged to read columns 1-4 of LIO to columns 15-18 of the buss as
shown in the following diagram .
FUNCTIONAL PLUGBOARD
Row 25 ooooo oo • • i« — • oooo ooooo ooooo BUSS
15 10 5
24
20
Row 26 ooooo ooooo ooooo ooooo o • • '• • LIO-OUT
24 21 20 15 10 5
(3) The SIO counter must be plugged so that:
(a) SIO-OUT I reads columns 5-24 of SIO to columns 5-24 of the buss;
(b) SIO-OUT II reads columns 1-4 of SIO to columns 1-4 of the buss;
as shown in the following diagram .
FUNCTIONAL PLUGBOARD
Row 34 o
Row 35 o
24
20
15
10
oooo BUSS
oooo SIO-OUT I
24
20
15
10
Row 36 ooooo ooooo ooooo ooooo o • t ,» • SIO-OUT II
24 20 15 10 5
Row 37 ooooo ooooo ooooo ooooo o •—•■
24 20 15 10 5
«-• BUSS
330
SOLUTION OF EXAMPLES
(4) The card feeds must be plugged direct (see page 272).
(5) The card punch must be plugged as shown in the following diagram,
PUNCH MAGNETS
5 10 15
(6)
20
•— •■
25
30
35
40
■•— •
OOOO OOOO 0000 oooo
45
50
55
60
OOOO OOOO OOOO OOOO
65
70
75
80
OOOO OOOO OOOO OOOO OOOO
COMP MAG OR GTR TOT EXIT OR M S IN
2A 2B 4A 4B 6A 6B
• • • • • • • • • •••■•••• • • • •
6B
•— ♦
■•— •
OOOO OOOO OOOO OOOO
Typewriter I must be plugged for positive or negative quantities, decimal point between columns
16 and 17, twelve digits to the right of the decimal point* The digits are to be grouped by fours
to the right and left of the decimal point, argument control after two decimal places. Line step
counter 1 is to be plugged for vertical groups of five lines. Typewriter II is to be plugged for
positive or negative quantities, decimal point between columns 16 and 17, eight digits to the
right of the decimal point. The digits are to be grouped by fours to the right and left of the deci-
mal point, argument control after two decimal places. Line step counter 2 is to be plugged for
vertical groups of five lines. The plugging for the typewriters is shown in the following diagram.
FUNCTIONAL PLUGBOARD
Row 1
KOW Z
DP TAB
4~ O
o •— •■
R TAB
• 000*
Row 3 o o o o o
*— •
A~
>^~T
20
SPACES
0*000
Row 4 o
Row 5
Row 6
■•— •
• 000
25 1
» o o o
10 I
ooo
30
r
40
•-U •— 1 • • •— 9-
15
• • •
o o o o o
35
45
-•OOOO
24
20
15
10
25 24
000 OOfOO OOOOO OOOOO 00000
20
15
10
• OOOO OOOOO
25 24 20
OOOOO OOOOO OOOOO
15
10
TYPEWRITER I
COL-SEL
PRINT CTR-RO
PRINT CTR-RO
RO-RELS
331
SOLUTION OF EXAMPLES
FUNCTIONAL PLUGBOARD
DP TAB
Row 8 * o o o o o •— »
Row 9
R TAB
Row 10 ooooo
Row 11 o • •<» •
■•— •
J •"•
20
SPACES
ooooo
10
25
T f
ooooo
30
24
20
•~o~oo
I ' i" I to
• ' • »-L> > i ■♦ i ooo ooooo
ooooo
40
t • # •
15
ooooo
35
ooooo
45
15
10
Row 12
2524
000 OOfOO ooooo ooooo ooooo
15
10
Row 13 Aoooo ooooo ooooo ooooo ooooo
25 24 15 10 5
Row 18 ooooo ooooo ooooo ooooo o o o • •-
2 1
Row 38 ooooo oooo •— , ooooo oooo
9 8 7 6 5
TYPEWRITER II
COL-SEL
PRINT CTR-RO
RO-RELS
Row 39 ooooo oooo
R
OOOOO OOOOS-,00000
4321 10 987654321 10
ooooo oooo^-looooQ
R
Example 8. It is to be noted that the starting and main control tapes of example 7 dictated only the
sequence of operations to be performed. The actual numbers dealt with; i.e„ arguments, functions,
coefficients, tolerances, etc., were delivered to the machine from switches and punch cards. In some
cases, these quantities were rearranged by plugging through which they passed on their way to and
from the functional components of the calculator. Obviously, then, the tapes themselves are applicable
to a whole class of problems of which example 7 is merely a special case. The reader is advised to
arbitrarily formulate several problems similar to example 7 involving other integrands, and to devise
the instructions necessary to the solution of the chosen problems on the calculator.
Example 9. It is required that a single main control tape be designed to tabulate the integral,
IW ^Vjdx,
as defined in example 7, where f(x) is the function defined in example 6. This requires the combination
332
SOLUTION OF EXAMPLES
of the control tapes designed for examples 3, 4, 5 and 7. The interweaving of the coding of the tapes
is left as an exercise for the reader. This computation as performed by a single control tape should
not require more than 110 seconds per tabulated value of the integral.
Example 10 . It is required that the series,
f(z) = a Q + a x z + a 2 z 2 + a g z 3 + ... + a n z n + R, (1)
be evaluated in the complex plane. The real coefficients a Q , aj, a 2 , a 3 , ..., a fl will be supplied from
a value tape on interpolator I. The complex quantities will be stored with the real and imaginary
parts in adjacent counters. Multiplication of a complex quantity by a real number requires two or-
dinary multiplications. The determination of an even power of a complex quantity requires three
ordinary multiplications, while the determination of an odd power requires four. The following coding
is designed to evaluate the first four terms of the series (1) for any point in the complex plane. The
coding has been planned, however, as though the series had many terms and required the conservation
of storage registers. The extension of the coding to care for terms involving powers of z greater
than the third is left to the reader as an exercise. The coding given in this example represents a sim-
plified version of the control tapes used to compute the modified Hankel functions of order one-third .
x or ax from sw. 1 to ctr. 1
.2
compute z
y or a y from sw. 2 to ctr. 2
a ft to ctr. 9 from interpolator I
Line
1 OUT
IN
MISC. 1
1
741
1
7
2
ll
761
7
3
j742
2
7
4
1 21
il
21
5
l»
7
6
Ui
41
7
7
85
753
8
41
9 J
21
7
10
|| 1
761
7
11
II 3
3
7
SOLUTION OF EXAMPLES
333
a 1 to ctr. 8 from interpolator I
compute a..z
compute z'
a« to ctr. 8 from interpolator I
Line
OUT
IN
MISC.
12
4
4
13
1
7
14
85
753
15
4
7
16
31
31
17
3
7
18
2
761
732
19
21
31
7
20
21
31
21
2
7
22
32
32
7
23
321
321
7
24
42
42
25
3
7
26
4
761
27
1
28
41
7
29
4
761
30
2
31
42
7
32
3
761
7
33
21
21
7
34
4
4
35
| 1
7
36
| 85
753
37
4
38
32
7
334
SOLUTION OF EXAMPLES
compute a«z*
a^ to ctr. 8 from interpolator I
compute agz'
a. to ctr. 8 from interpolator I
X-line
! w
39
31
761
32
40
2
41
32
7
42
3
761
43
2
44
321
7
45
31
761
46
1
47
321
n
48
4
761
49
3
50
41
7
51
4
761
7
1 52
4
4"
i 53
131
i
7
54
1 85
1 753
55
!
4
56
42
7
57
4
761
58
32
59
41
*7
60
4
761
7
61
4
4
62
321
7
63
85
753
64
4
65
_____
J
42
7
335
SOLUTION OF EXAMPLES
Example 11 . It is suggested that the reader code the control tapes necessary for the computation and
checking of a functional tape for f(x) = arc sin x, < x S 0.9. The error in the interpolated values of
f(x) should be less than 6 x 10" 11 . The following control tapes should be coded:
(a) starting and main control tapes to compute the interpolational coefficients;
(b) control tape to position the functional tape to the successive arguments and print the coef-
ficients;
(c) control tape to interpolate on assigned values of the argument.
The control tape to compute the interpolational coefficients should use an iterative process for the
computation of (1 - x 2 )" 1/2 . The iterative formulae and their codings are given on pages 176-179 and
in example 4, pages 304-312. The number of interpolational coefficients required is discussed on
pages 198-199. The coding of the control tapes necessary to check the functional tape is presented
on pages 199-201.
Example 12. The Bessel function, J Q , has been computed for an increment of the argument equal to
0.01, and punched in tabulating machine cards. It is suggested that the reader code the control tapes
necessary to subtabulate the function to tenths; i.e., for increment of the argument equal to 0.001.
The tape must, of course, completely check the computation and verify the printed results. Such a
tape, using the method described on pages 224-226, has been preserved in the tape library after being
used to subtabulate the Bessel functions 2 .
Example 13 . It is suggested that the reader design a control tape for the solution of the system of
linear algebraic equations,
a l,l X l +a l,2 X 2 + "' + a l,10 X 10 =k l .
a 2,l x l +a 2,2 X 2 + - + a 2,10 X 10 = k 2
a 10,l X l + a 10,2 X 2 + - + ho^lO = k 10'
by the process of successive elimination. The elements of the given matrix must be manually punched
in tabulating machine cards and stacked in two decks, one for the a- ., in the order a , ..., a
a 2,l> •••» a 2,10' •••» a 10,l' "•' a 10,10> and the other for the k i» in the order k p k 2 , »., k 10 .
336
SOLUTION OF EXAMPLES
Assume the card decks containing the a- - and the k, to be placed in card feeds I and II respec-
i,] 1
tively. A main control tape may then dictate the following operations:
(1) feed 10 cards from card feed I to any 10 storage counters;
(2) feed 1 card from card feed II to any other storage counter;
(3) take the reciprocal a« « ;
(4) multiply a 1 2 , a x 3 , ..., z 1 1Q and kj by 1/aj jj
(5) feed 10 cards from card feed I to any 10 storage counters not already in use;
(6) feed 1 card from card feed II to any storage counter not already in use;
(7) using the quantities read into storage counters in (5) and (6), repeat operations (3) and (4)
for a <t a„ „, ..., a„ «_ and k„;
2,1 2,6 <5,1U 4
(8) make the necessary subtractions;
(9) repeat these operations until the given system is reduced to the form
x l + b l,2 x 2 + b l,3*3 + — + b l,10 x 10 = h l
x 2 + b 2,3 x 3 + •" + b 2,10 x 10 = ^2
x 10 " h 10
whexe tn6 b. . <tiid the h. &utiid in 55 ^elected storage counters;
1,J 1
(10) the values of the xj may then be obtained by substitution and printed or punched in tabu-
lating machine cards for further computation.
For efficient operation, full advantage must be taken of the methods of interposition, and all operations
must be checked. The computation and comparison of 2 a.- ^/a* , and (Ha. .)/a. < is one form of
check procedure.
The required control tape includes 4964 lines of coding, produces and completely checks the
values of x^ in approximately 55 minutes. The tape is one of the standard tapes preserved in the tape
library.
Nearly two years have passed since the staff of the Computation Laboratory of Harvard Univer-
sity began operation with the Automatic Sequence Controlled Calculator as a project of the United
States Navy. During this time, a great variety of problems has been solved finding application in
337
SOLUTION OF EXAMPLES
nearly every branch of physics and engineering. The problems solved include:
the tabulation of functions of a real variable defined by given equations;
the subtabulation of empirical functions;
the computation and tabulation of quantities defined by elaborate formulae and in terms of
empirical variables;
(4) the tabulation of functions in the complex domain;
(5) the solution of systems of linear algebraic equations;
(6) statistical analysis;
(7) the determination of the zeros of functions;
(8) the evaluation of definite integrals ;
(9) the solution of systems of ordinary differential equations;
(10) the solution of partial differential equations.
As previously mentioned, the examples given in this chapter have been chosen for their mathe-
matical simplicity. However, the solutions of the problems listed in the foregoing tabulation have all
been obtained by means of extensions of the techniques illustrated in the examples .
From time to time, the solution of these problems has required permanent changes in the wiring
of the calculator, and the inclusion of new features, many of which have greatly improved its oper-
ation. Such improvements and alterations are still in progress of development. As a result, this
book goes to press representing the standard procedure of the Computation Laboratory as of August
1945.
References
1 . Annals of the Computation Laboratory of Harvard University, Volume n, Tables of the Modified
Hankel Functions of Order One -Third and of Their Derivatives, Harvard University Press,
Cambridge, Mass., 1945, xxxvi + 235 p.
2. Annals of the Computation Laboratory of Harvard University, Volume III, Bessel Functions of
Orders Zero and One, to be published by the Harvard University Press in 1946.
Annals of the Computation Laboratory of Harvard University, Volume IV, Bessel Functions of
Orders Two and Three, to be published by the Harvard University Press in 1946.
338
BIBLIOGRAPHY
OF
NUMERICAL ANALYSIS
In practice, a computational problem is composed of three parts: the theoretical mathematical
analysis j the construction of a numerical computational schedule suitable for the particular calcula-
ting machines to be used; the actual carrying out of the machine computation. In connection with the
first two parts, it is necessary to consult widely scattered mathematical literature in an effort to
find adequate methods to treat new types of problems of applied mathematics. These methods have to be
further adapted to take full advantage of large scale calculating machinery.
In the preparation of this bibliography, full use has been made of available published bibli-
ographies, particularly those contained in the report on numerical methods by H. Bateman, W. E. Milne
and A. A. Bennett (see Ordinary Differential Equations). The bibliography is not intended to be ex-
haustive. It is composed principally of the references that have been found useful during the one and
one-half years of operation of the Automatic Sequence Controlled Calculator.
In the bibliography, certain subjects that logically fall within the general field of numeri-
cal analysis have been omitted, for example, no mention is made of statistics. Such references as
have been included, however, have been classified for ready reference. Some of the titles could be
listed under several headings, and have been in the more important cases.
1. Historical Background of Automatic Calculating Machinery
2. Machine Methods in Arithmetic
3. General Numerical Methods
6. Square Roots and Higher Roots of Numbers
7. The Location and Separation of the Zeros of a Polynomial
8. The Calculation of the Zeros of a Polynomial
A. Iterative Methods (Newton-Raphson, False Position, etc.)
B. Root-Squaring and Allied Methods
C. Miscellaneous Methods
9« The Zeros of Transcendental Equations
A. Iterative Methods (see also under 8A)
6. Miscellaneous Methods
339
BIBLIOGRAPHY
10. Implicit Functions
11. Harmonic Analysis
12. Periodogram Analysis
13. Finite Differences
14. Difference Equations
15. Direct Interpolation
A. Functions of a Single Variable
B. Functions of Several Variables
16. Inverse Interpolation, Tabulation and Subtabulation
17. Interpolation Tables
18. Asymptotic Expansions
19. Numerical Differentation and Higher Derivatives
20. Numerical Integration of Definite Integrals
A. Functions of a Single Variable
B. Functions of Several Variables
21. Ordinary Differential Equations
22. Partial Differential Equations
23. Integral Equations
1. HISTORICAL BACKGROUND OF AUTOMATIC CALCULATING MACHINERY
BABBAGE, C. On the Economy of Machinery and Manufactures. London, 1846.
BABBAGE, C. Passages from the Life of a Philosopher. London, 1864.
BAXANDALL, D. Catalogue of the Collections in the Science Museum, South Kensington. Mathematics I,
Calculating Machines and Instruments. London, 1926.
CAJQRI, F. A History of Mathematics. New York, 2nd ed. 1919.
CAJORI, F. History of the Logarithmic Slide Rule. New York, 1909.
CAJORI, F. William Oughtred. Chicago, 1916.
DYCK, W. Katalog mathematischer und mathematisch-physikalischer Modelle, Apparate und Instrumente.
Munich, 1892.
GALLE, A. Mathematische Instrumente. Leipzig, 1912.
HORSBURGH, E. M. Calculating machines. A Dictionary of Applied Physics. Richard Glazebrook ed.
London, 1923, vol. 3, p. 193-201.
HORSBURGH, E. M. Modern Instruments and Methods of Calculation. London, 1914.
JACOB, L. Le calcul mecanique. Paris, 1911.
D'OCAGNE, M. Le calcul simplified Paris, 1905 .
340
BIBLIOGRAPHY
D'OGAGNEj M- Tue d' ensemble sur les machines a calculer, Paris. 1922.
POSSELT, E, A. The Jacquard Machine. Philadelphia, 189-?.
TURCK, J. A. V. Origin of Modern Calculating Machines. Chicago, 1921.
2. MACHINE METHODS IN ARITHMETIC
COMRIE, L. J. Mechanical computing. Appendix I, p. 462-473 of David Clark, Plane and Geodetic Sur-
veying, vol. 2, 3rd ed., revised by James Glendenning. London, Constable, 1943.
COMRIE, L. J. Recent progress in scientific computing. Jour. Sci. Instr. 21, 129-135 (1944).
HARTKEMEIER, H. P. and MILLER, H. E. Obtaining differences from punched cards. Jour. Amer. Statist.
ASSOC. J>f, £.0?—<X>( \XJtt*.J»
KNUDSEN, L. F. A punched card technique to obtain coefficients of orthogonal polynomials. Jour.
Amer. Statist. Assoc. 37, 496-506 (1942).
LANCASTER, 0. E. Machine method for the extraction of cube root. Jour. Amer. Statist. Assoc. 37,
112-115 (1942).
McPHERSON, J. C. On mechanical tabulation of polynomials. Ann. Math. Statist. 12, 317-327 (1941).
McPHERSON, J. C. Mathematical operations with punched cards. Jour. Amer. Statist. Assoc. 37, 275-
281 (1942).
SANDOMIRE, M. M. Accumulating cubes with punch cards. Jour. Amer. Statist. Assoc. 36, 507-514 (1941).
3. GENERAL NUMERICAL METHODS
n ii
BLERMANN, 0. Vorlesungen uber mathematischen Naherungsmethoden. Braunschweig, Vieweg, 1905, 226 p.
BRUNS, H. Grundlinien des wissenschaftlichen Rechnens. Leipzig, Teubner, 1903, 159 p.
CASSINIS, G. Calcoli numerici, grafici e meccanici. Pisa, Mariotti-Pacini, 1928, xix + 672 p.
CAS3INA, U. Calcoio numerico con numerosi esempi e note storiche original! . Bologna, Zanicheili,
1928, xix + 453 p.
COURANT, R. Differential and Integral Calculus. (New revised edition) New York, Nordemann, 1940,
vol. 1, chap. 7, p. 342-364.
HAYASHI, K. Tafeln fur die Differenzenrechnung... Berlin, Springer, 1933, vi + 66 p.
LEHMER, D. H. On the value of the Napierian Base. Amer. Jour. Math. 48, 139-143 (1926).
LEHMER, D. N., BALLANTINE, J. P. and THOMPSON, D'A. W. On the multiplication of long decimals. Amer.
Math. Month. 30, 67-69 (1923).
LINDOW, M. Numerische Infinitesimalrechnung. Berlin and Bonn, Dunsnler, 1928, viii + 176 p.
LUROTH, J. Vorlesungen uoer numerisches Rechnen. Leipzig, Teubner, 1900, vi + 194 p.
MACCAFERRI, E. Calcoio numerico approssimato. Milan, Hoepli, 1919, 200 p.
MADER, K. Numerisches Rechnen. Handbuch der Physik.vol. 3. Berlin, Springer, 1928, p. 599-635.
341
BIBLIOGRAPHY
MAYER, J. £. Das Rechnen in der Technlk und seine Hilfsmittel. Vol. 405 of Sammlung Goschen. Leipzig,
Goschen, 1st ed. 1908; 2nd ed. 1913, 128 p.
MILNE-THOMPSON, L. M. Calculus of Finite Differences. London, Macmillan, 1933, xxiii + 558 p.
PESCI, G. ...Numeri decimali approssimati... Period. Mat.: (3) 1, 249-268; (3) 2, 1-21, 49-71
(1904).
RADAU, R. Etude sur les formules d' interpolation. Paris, Gauthier-Villars, 1891, 96 p.
RICE, H. L. Theory and Practice of Interpolation. Lynn, Nichols, 1899, 234 p.
RUNGE, C. and KONIG, H. Vorlesungen uber Numerisches Rechnen. Berlin, Springer, 1924, viii+371 p.
VON SANDEN, H. Praktische Analysis. Leipzig, Teubner, 2nd ed. 1923, xvi + 195 p.
VON SANDEN, H. Mathematisches Praktikum. I. Leipzig, Teubner, 1927, v + 122 p.
SCARBOROUGH, J. B. Numerical Mathematical Analysis. Baltimore, Johns Hopkins Press, I930,xiv+416 p.
SCHRUTKA, L. Zahlenrechnen. Leipzig, Teubner, 1923, 146 p.
SHEPPARD, W. F. Mensuration. Encyclopaedia Britannica. 14th ed. 1929, vol. 15, p. 253-257.
STEFFENSEN, J. F. Interpolation. Baltimore, Williams and Wilkins, 1927, ix + 248 p.
THIELE, T. N. Interpolationsrechnung. Leipzig, Teubner, 1909, 175 p.
UHLER, H. S. Multiplication of large numbers. Amer. Math. Month. 28, 447-448 (1921).
VAHLEN, T. Konstruktionen und Approximationen. Leipzig, Teubner, 1911, xii +349 p.
WHTTTAKER, E. T. and ROBINSON, G. The Calculus of Observations. A Treatise on Numerical Mathematics.
London and Glasgow, Blackie, 3rd ed. 1940, xvi + 395 p.
WILLERS, F. A. Methoden der Praktischen Analysis. Berlin, de Gruyter, 1928, 344 p.
WORTHING, A. G. and GEFFNER, J. Treatment of Experimental Data. New York, Wiley, 1943, ix + 342 p.
XAVIER, A. Theorie des approximations numeriques et du calcul abrege. Paris, Gauthier-Villars, 1909.
ZORETTI, L. ^ Exercices numeriques et graphiques de mathematiques sur les leqons de mathematiques
generales. Paris, Gauthier-Villars, 1914, xv + 124 p.
4. LINEAR ALGEBRAIC EQUATIONS, DETERMINANTS AND MATRICES.
AITKEN, A. C. Studies in practical mathematics. II. The evaluation of the latent roots and latent
vectors of a matrix. Proc. Roy. Soc. Edin., Sect. A, 57, 269-304 (1936-1937).
BELLMAN, R. A note on determinants and Hadamard's inequality. Amer. Math. Month. 50, 550-551 (1943).
BINGHAM, M. D. A new method for obtaining the inverse matrix. Jour. Amer. Statist. Assoc. 36, 530-
534 (1941).
BISSHOPP, K. E. The inverse of a stiffness matrix. Quart. Appl. Math. 3, 82-84 (1945).
BRAND, L. The method of moment distribution for the analysis of continuous structures. Bull. Amer.
Math. Soc. 41, 901-906 (1935).
CHIO, F. Memoirs sur les fonctions connues sous le nom de re'sultantes ou de determinants. Turin.
1853.
342
BIBLIOGRAPHY
COLLAR, A„ R. On the reciprocation of certain matrices- Proc. Roy. Soc- Edin. 59, 195-206 (1939).
COLLATZ, L. Fehlerabschatzung fur das Iterationsverfahren zur Auflosung linearer Gleichungssysteme.
Zeit. Angew. Math. Mech. 22, 357-361 (1942).
COURANT, R. and HILBERT, D. Methoden der Mathematischen Physik. Vol. I. Berlin, Springer, 2nd ed.
1931, adv + 469 p., chap. I.
CROSS, H. Analysis of continuous frames by distributing fixed-end moments. Paper No. 1793. Trans.
Amer. Soc. Civil Engrs. 96, 1-10 (1932).
DRESDEN, A. On the iteration of linear homogeneous transformations. Bull. Amer. Math. Soc. 48, 577-
579, 949 (1942).
DWYER, P. S. The evaluation of multiple and partial correlation coefficients from the factorial ma-
trix. Psychometrika 5, 211-232 (1940).
DWTER, P. S. The solution of simultaneous equations. Psychometrika o, 101—129 v.1941,/.
DWTER, P. S. The evaluation of determinants. Psychometrika 6, 191-204 (1941).
TTBJTET? P . R .
—••-■—-, . . — .
DWTER, P. S. The Doolittle technique. Ann. Math. Statist. 12, 449-458 (1941).
ERIKSSON, H. A. S. A technique for the approximate calculation of eigenvalues as zeros of a de-
terminant. Application to the Li + -ion in the ground state. Arkiv for Mat. 30B, No. 6, 8 p.
(1944) .
ETHERINGTON, I. M. H. On errors in determinants. Proc. Edin. Math. Soc. (2) 3, 107-117 (1932).
FARNELL, A. B. Limits for the characteristic roots of a matrix. Bull. Amer. Math. Soc. 50, 789-794
(1944).
FRAZER, R. A., DUNCAN, W. J. and COLLAR, A. R. Elementary Matrices and some Applications to Dynamics
and Differential Equations. Cambridge, Cambridge Univ. Press. 1938. p. 96-I33.
FREEMAN, G. F. On the iterative solution of linear simultaneous equations. Phil. Mag. (7) 34, 409-
416 (1943).
HADAMARD, J. Resolution d'une question relative aux determinants. Bull. Sci, Math. (2) 17, 240-246
(1893).
HOELj P- G. The errors involved in evaluating correlation determinants, Ann, Math. Statist. 11, 58-
65 (1940).
HOEL, P. G. On methods of solving normal equations. Ann. Math. Statist. 12, 354-359 (1941).
HOPSTEIN, N. M. Solution of homogeneous linear equations by the iteration method. C. R. (Doklady)
Acad. Sci. URSS (N.S.) 43, 372-575 (1944).
HORST, P. A non-graphical method for transforming an arbitrary factor matrix into a simple structure
factor matrix. Psychometrika 6, 79-99 (1941).
HOTELLING, H. Simplified calculation of principal components. Psychometrika 1, 27-35 (1936).
HOTELLING, H. Some new methods in matrix calculation. Ann. Math. Statist. 14, 1-34 (1943).
HOTELLING, H. Further points on matrix calculation and simultaneous equations. Ann. Math. Statist.
14, 440-441 (1943).
IVANOV, V. On the convergence of the process of iteration in the solution of a system of linear
algebraic equations. (Russian. English summary.). Bull. Acad. Sci. URSS Ser. Math.(lzvestia
L\ra* Mnnfc- RSR!^ 10*50 I.V7- l.*M flcyiO\
343
BIBLIOGRAPHY
LEVY, S. Buckling of rectangular plates with built-in edges. Jour. Appl. Mech. 9, A171-A174 (1942).
LONSETH, A. T. Systems of linear equations with coefficients subject to error. Ann. Math. Statist.
13, 332-337 (1942).
LONSETH, A. T. On relative errors in systems of linear equations. Ann. Math. Statist. 15, 323-325
(1944).
MEHMKE, R. Uber das Seidel'sche Verfahren, urn lineare Gleichungen bei einer sehr grossen Anzahl der
Unbekannten durch successive Annaherung aufzulosen. Math. Samml. Mosk. 16, 4 p. (1892).
MEHMKE, R. and NEKRASSOFF, P. A. Auflosung eines linearen Systems von Gleichungen durch successive
Annaherung. Math. Samml. Mosk. 16, 23 p. (1892).
MEIHEKE, H. Naherungsformel fur die Berechnung von Strecken. Zeit. Angew. Math. Mech. 20, 359 (1940).
MILNE-THOMPSON, L. M. Determinant expansions. Math. Gaz. 25, 130-135 (1941).
MORRIS, J. and HEAD, J. W. Lagrangian frequency equations. An "escalator" method for numerical
solution. Aircraft Engrg. 14, 312-314, 316 (1942).
OLDENBURGER, R. Convergence of Hardy Cross's balancing process. Jour. Appl. Mech. 7, A166-A170(1940).
PARKER, W. V. Limits to the characteristic roots of a matrix. Duke Math. Jour. 10, 479-482 (1943).
PIPES, L. A. The solution of a.c. circuit problems. Jour. Appl. Phys. 12, 685-691 (1941).
REIERS0L, 0. A method for recurrent computation of all the principal minors of a determinant, and
its application in confluence analysis. Ann. Math. Statist. 11, 193-198 (1940).
RICE, L. H. Some determinant expansions. Amer. Jour. Math. 42, 237-242 (1920).
RUHGE, C. and KONIG, H. Vorlesungen uber numerisches Rechnen. Berlin, Springer, 1924, p. 183-188.
SAIBEL, E. A modified treatment of the iterative method. Jour. Franklin Inst. 235, 163-166 (1943).
SAIBEL, E. A rapid method of inversion of certain types of matrices. Jour. Franklin Inst. 237. 197-
201 (1944).
SAMUELSON, P. A. A method of determining explicitly the coefficients of the characteristic equation.
Ann. Math. Statist. 13, 424-429 (1942).
SATTERTHWAITE, F. E. Error control in matrix calculation. Ann. Math. Statist. 15, 373-387 (1944).
SCHMIDT, R. J. On the numerical solution of linear simultaneous equations by an iterative method.
Phil. Mag. (7) 32, 369-383 (19a).
I! II
SCHULZ, G. Uber die Losung von Gleichungssystemen durch Iteration. Zeit. Angew. Math. Mech. 22. 234-
235 (1942). 6 '
SEIDEL, L. ff Oeber ein Verfahren, die Gleichungen, auf welche die Methods der kleinsten Quadrate
fuhrt, sowie lineare Gleichungen Uberhaupt, durch successive Annaherung aufzulosen. Abh.
Akad. Munchen 11 (III), 81-108 (1874).
SEMENDIAEV, K. A. The determination of latent roots and invariant manifolds of matrices by means of
iterations. (Russian. English summary.). Appl. Math. Mech. (Akad. Nauk SSSR. Prikl. Mat.
Mech.) 7, 193-222 (1943).
SOUTHWELL, R. V. Stress calculations in frame-works by the method of systematic relaxation of
constraints, I, II; III. Proc. Roy. Soc. Lond.: A151, 56-95; AI53, 41-76 (1935).
SPOERL, C. A. A fundamental proposition in the solution of simultaneous linear equations. Trans.
Actuar. Soc. Amer. 44, 276-288 (1943).
344
BIBLIOGRAPHY
SPQERL, G» A* On solving sijntiltaneous linear equations. Trans. Actuar, Soc. Amer. 45, 18-32. 67-69
(1944). ^
SYNGE, J. L. A geometrical interpretation of the relaxation method. Quart. Appl. Math. 2, 87-89
(1944).
TUCKER, L. E. The determination of successive principal components without computation of tables
of residual correlation coefficients. Psychometrika 9, 149-153 (1944).
TUCKERMAN, L. B. On the mathematically significant figures in the solution of simultaneous linear
equations. Ann. Math. Statist. 12, 307-316 (1941).
TURAN, P. On extremal problems concerning determinants. (Hungarian. English summary.). Math. Natur-
wiss.An2. Ungar. Akad. Wiss. 59, 95-105 (1940).
TURTON, F. J. On the solution of the numerical simultaneous equations arising in the analysis of re-
dundant structures. Jour. Roy. Aeronaut. Soc. 49, 104-111(1945).
ULLMAN, J. The probability of convergence of an iterative process of inverting a matrix. Ann. Math.
Statist. 15, 205-213 (1944).
WATLAND, H. Expansion ox ueteHBin&iital equatj.ons into poxynosnxax ronn. v*aru. Appx. «aun. »., —sc
306 (1945).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 3rd ed. 1942,p.
71-77.
WH1TTAKER, E. T. and WATSON, G. N. A course of Modern Analysis. Cambridge, Cambridge Univ. Press,
Amer. ed. 1944, p. 212-213.
WRIGHT, L. T., Jr. The solution of simultaneous linear equations by an approximation method. Cornell
Univ* Engrg, Exper, Station, Bull* No, 31, 1943, 6 p.
BANACHIEWICZ, T. An outline of the Cracovian algorithm of the method of least squares. Astr. Jour.
50, 38-41 (1942).
BERJMAN, E. A solution of the problem of least squares adjustment by Gauss polynomials. (Spanish).
An. Soc. Ci. Argentina: 132, 34-48, 104-117, 212-217 (1941); 133, 208-215, 442-445 (1942).
BIRGE, R. T. and SHEA, J. D. A rapid method for calculating the least squares solution of a poly-
nomial of any degree. Univ. of Calif. Pubis. Math. 2, No. 5, 1927, p. 67-118.
BLEICK, W. E. A least squares accumulation theorem. Ann. Math. Statist. 11, 225-226 (1940).
DAVIS, H. T. Polynomial approximation by the method of least squares. Ann. Math. Statist. 4, 154-
196 (1933).
DAVIS, H. T. and LATSHAW, V. V. Formulas for the fitting of polynomials by the method of least
squares. Ann. of Math. (2) 31, 52-78 (1930).
DWYER, P. S. A matrix presentation of least squares and correlation theory with matrix justification
of improved methods of solution. Ann. Math* Statist. 15, 82-89 (1944).
IDELSON, N. On the computation of weights of the unknowns in the method of least squares. ^Russian.
English summary.). Astr. Jour. Soviet Union 20, 11-13 (1943).
JACKSON, D. The Theory of Approximation. New York, Amer. Math. Soc. Colloq. Pubis, vol. XI (Amer.
Math. Soc.) 1930, viii + 178 p.
345
BIBLIOGRAPHY
KERAWALA, S. M. A rapid method for calculating the least squares solution of a polynomial of degree
not exceeding the fifth. Indian Jour. Phys. 15, 241-276 (1941).
LEVENBERG, K. A method for the solution of certain non-linear problems in least squares. Quart.
Appl. Math. 2, 164-168 (1944).
NAUt, K. R. and SHRIVASTAVA, M. P. On a simple method of curve fitting. Sankhya 6, 121-132 (1942).
PLARR, G. Note sur une propriete commune aux series dont le terme general depend des f onctions X^
de Legendre, ou des cosinus et sinus des multiples de la variable. C. R. Acad. Sci. Paris
44, 984-986 (1857).
REMES, E. J. Sur les approximations par les moyennes d'ordre 2k et celles d'aprSs le principe des
moindres carres. (Russian. French summary.). Rec. Math. (Mat. Sbornik) N.S. 9 (51) 437-450
(1941) .
STONER, P. M. Fitting the exponential function and the Gompertz function by the method of least
squares. Jour. Amer. Statist. Assoc. 36, 515-518 (1941).
6. SQUARE ROOTS AND HIGHER ROOTS OF NUMBERS
BOORMAN, J. M. Evolution simplified: Square root found by addition instead of division. Math. Mag.
(publ. Artemas Martin) 1, 112-115 (1882-1884).
DEDERICK, L. S. A modified method for cube roots and fifth roots. Amer. Math. Month. 33, 469-472
(1926) .
VON FEHRENTHEIL und GRUPPENBERG, L. R. Vereinfachte Quadratwurzelziehung mit der Rechenmaschine.
Zeit. Instrumentenkunde 62, 227-230 (1942).
HOFMANN, J. E. Uber ein "neues" Verfahren zur Annaherung von QuadratTiurzeln und seine geschichtliche
Bedeutung. Deutsche Math. 6, 453-461 (1942) .
HUSSAIN, S. T. A method of extracting the nth root of a positive number. Math. Student 11. 12-15.
(1943). '
LANCASTER, 0. E. Machine method for the extraction of cube root. Jour. Amer. Statist. Assoc. 37.
112-115 (1942). '
LEHMER, D. H. On the use of the calculating machine for cube and fifth roots. Amer. Math. Month.
32, 377-379 (1925).
■t
LORET, W. Uber ein Eulersches Verfahren zur Wirzelberechnung. Monatsh. Math. Phys. 48, 190-197
vl939y .
MARTIN, A. Computation of the cube root of 2. Mess, of Math. 7, 50-51 (1878).
MARTIN, A. Extraction of square roots by series. Math. Mag. 1, 164-165, 172 (1882-1884).
S. First-prize solution to problem of the be*
to 100 decimals. Math. Visitor 2 (#2), 31 (1883).
', G. W. Successive approximations to n /a7 Math. Gaz. 17, 52-53, 127 (1933).
PUTNAM, K. S. First-prize solution to problem of the best formula for \ 3 /~x". To illustrate by ?/~2~
to 100 decimals. Math. Visitor 2 (#2). ■?! (I8#rt. V * V
WARD
7. THE LOCATION AND SEPARATION OF THE ZEROS OF A POLYNOMIAL
ANGHELUTZA, T. Sur une limite des modules des zeros des polynomes. Acad. Roum. Bull. Sect. Sci.
21, 211-213 (1939).
346
BIBLIOGRAPHY
APiRfi. E- Di alcuae awertenze sulla risoluzione numerica delle equazioni algebriche. Univ. Roma e
"' " 1st. Naz. Alta Mat. Rend. Mat. e Appl. (5) 4, 125-147 (1943).
B3EBERBACH, L. Vorlesungen uber Algebra. Leipzig and Berlin, Teubner, 1928, p. 171, 186.
BIEBERBACH, L. Lehrbuch der Funktibnentheorie. Leipzig and Berlin, Teubner, 1930, vol.1, p. 190-192.
SUDAN, D. Nouvelie mefchode pour la resolution des equations numeriques... Paris, 2nd ed. 1822.
BURNSIDE, W. S. and PANTON, A. W. Theory of Equations. Dublin, Hodges and Figges, 8th ed. 1918, vol.
I, chap. 10, 11.
CARACCIOLO, M. S. Delle equazioni a radici opposte. Boll. Mat. (4) 1, 33-38 (1940).
CAUGHT, A. L. Analyse algebrique. Note III. See Oeuvres completes d'Augustin Cauchy, (2) vol. 3.
Paris, Gauthier-Villars, 1897, p. 378-425.
Cauuhi, a. ju. fixercices ae ma-wiemaTixques. See ueuvres, \<e.j vux. y, rafxo, A071, y ^JT-^j-t -.•-.--•-.
GOHN, A. Uber die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise. Math. Zeit. 14,
110-148 (1922).
CONKWRIGHT, N. B. An elementary proof of the Budan-Fourier theorem. Amer. Math. Month. 50, 603-605
(1943).
COPSON, E. T. An Introduction to the Theory of Functions of a Complex Variable. Oxford, Oxford
Press, 1935, P. 119-121.
CORLISS, J. J. Upper limits to the real roots of an algebraic equation. Aiaer. Math. Month. 46, 334-
338 (1939).
DELANGE, R* Sur la convergence des series de polynomes de la forme £ *rP R (*) «t sur certaines suites
de polynomes. Ann. Ecole Norm. Sup. 56, 173-275 (1939).
FEJER, L. Uber die Wurzel vom kleinsten absoluten Betrage einer algebraischen Gleichung. Math. Ann.
FOURIER, J. B. J. Analyse des equations determinees. Paris, Didot, 1830, xxiv + 258 p.
FRAZER, R. A., DUNCAN, W. J. and COLLAR, A. R. Elementary Matrices and Some Applications to Dynamics
and Differential Equations. Cambridge, Cambridge Univ. Press, 1938, p. 151-155.
FRICKE, R. Lehrbuch der Algebra. Braunschweig, Vieweg, 1924, vol. I part 2, chap. 3.
GENOCCHI, A. Demonstration d'un thebreme de M. Sylvester. Nouv. Ann. Math. (2) 6, 6-20 (1867).
HERGLOTZ, G. Uber die Wurzelanzahl algebraischer Gleichungen innerhalb una auf dem Einheitskreis.
Math. Zeit. 19, 26-34 (1923).
HURW1TZ, A. Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen
Theilen besitzt. Math. Ann. 46, 273-284 (1895).
KHARADSE, A. Eine Anwendung des Graceschen Faltungssatzes. (Russian. German summary.). Mitt. Georg.
Abt. Akad. Wiss. USSR 1, 175-180 (1940).
KNESER, H. Zur Stetigkeit der Wurzeln einer algebraischen Gleichung. Math. Zeit. 48, 101-104 (1942).
KONIG, J. Ein allgemeiner Ausdruck fur die ihrem absoluten Betrage nach kleinste Wurzel der Gleich-
ung n-ten Grades. Math. Ann. 9, 530-540 (1875-1876).
n
KRONECKER, L. Uber Systeme von Functionen mehrer Variablen. Ges. Werke, vol. I. Leipzig, Teubner,
1895, p. 177-226.
KRONECKER, L. Uber die verschiedenen Sturm' schen Reihen und ihre gegenseitigen Beziehungen. Ges.
Werke, vol. I. Leipzig, Teubner, 1895, p. 305-348.
347
BIBLIOGRAPHY
KRQNECKER, L. Sur le thebreme de Sturm. Ges. Werke vol. I. Leipzig, Teubner, 1895, p. 229-234.
KRONECKER, L. Uber die Charakteristik von Functionen-Systemen. Ges. Werke vol. II. Leipzig, Teubner,
1897, p. 71-82.
LAGRANGE, J. L. De la resolution des equations numeriques de tous les degres. Paris, Duprat, 1798,
vii + 268 p., chap. I, p. 4-20; Note iv, p. 124-135 J Note viii, p. 165-180.
_~ « it
LIPKA, S. Uber die Abzahlung der reellen Wurzeln von algebraischen Gleichungen. Math. Zeit. 47, 343-
351 (1941).
it
LIPKA, S. Uber die Yorzeichenregeln von Budan-Fourier und Descartes. Jber. Deutsch. Math. Verein.
52, 204-217 (1942).
MADHAVA RAO, B. S. and SASTRY, B. S. On the limits for the roots of a polynomial equation. Jour.
Mysore Univ. Sect. B. Vol. I, 5-8 (1940).
MAHKOFF, A. On the determination of the number of roots of an algebraic equation, situated in a
given domain. Rec. Math. (Mat. Sbornik) N. S. 7 (49), 3-6 (1940).
MAXIMOFF, I. On neighboring roots. C. R. (Doklady) Acad. Sci. URSS (N. S.) 37, 88-90 (1942).
MONTEL, P. Observation sur la communication precedente. C. R. Acad. Sci. Paris 210, 654-655 (1940).
MONTGOMERY, J. C. The roots of a polynomial and its derivative. Bull. Amer. Math. Soc. 47, 621-624
(1941).
NEWTON, I. Universal Arithmetick. (Translation and revision by Mr. Ralphson and Mr. Cunn of Arith-
metica Universalis) London, 1728, iii + 271 p., p. 190-198, 204-208.
n
OBRESCHKOFF, N. Uber algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen.
Math. Zeit. 45, 747-750 (1939).
OSTROWSKI, A. Sur la continuite" relative des racines d»equations algebriques. C. R. Acad. Sci. Paris
209, 777-779 (1939).
PASCAL, E. Repertorium der hoheren Mathematik. Vol. I (1). Leipzig, Teubner, 2nd ed. 1910, p. 349-
352.
PERRON, 0. Algebra, Berlin, de Gruyter, 2nd ed. 1927, vol. II, chap. I.
PHRAGMEN, E. Sur une extension du thebreme de Sturm. C. R. Acad. Sci. Paris 114, 205-208 (1892).
PUND, 0. Algebra... Vol. 6 of Sammlung Schubert. Leipzig, Goschen, 1899, viii + 345 p., p. 243-267.
RUNGE, C. Gleichungen. Separation und Approximation der Wurzeln. Ency. Math. 7?iss., Leipzig,
Teubner, 1899, I B 3a sections 2-9, p. 407-432.
SERGESCU, P. Sur les limites de J. J. Bret. C. R. Acad. Sci. Paris 210, 652-654 (1940).
SERGESCU, P. Generalisations des limites de J. J. Bret. Acad. Roum. Bull. Sect. Sci. 22, 460-465
(1940).
n
SPECHT, W. Wurzelabschatzungen bei algebraischen Gleichungen, Jber. Deutsch. Llath. Verein. 49, 179-
190 (1940).
STERN, M. A. Uber die Anwendung der Sturmschen Methode auf transcendente Gleichungen. Jour. Reine
Angew. Math. 33, 363-365 (1846).
STURM, C. Memoire sur la resolution des equations numeriques. Par. Mem. Sav. (Etr.) 6, 271-318
(1835).
348
BIBLIOGRAPHY
SYLVESTER, J* J« On an improved form of statement of a new rule for the separation of the roots of
'analeebraical equation, with a postscript containing a new theorem. Phil. Mag. (4) 31,
214-218 (1866).
VON SZ. NAGY, G. 5ber ganze Funktionen mit lauter reellen Nullstellen. Univ. Nac. Tucuman. Revista
A. 1, 303-311 (1940).
TERRACINI, A. Some elementary remarks concerning the reality of the roots of an algebraic equation.
(Spanish). Math. Notae 4, 137-144 (1944).
THOMAS, J. M. Sturm's theorem for multiple roots. Nat. Math. Mag. 15, 391-394 (1941).
THUE, A. Ein Fundamentaltheorem zur Bestimmung von Annaherungswerten aller Wurzeln gewisser ganzer
Funktionen. Jour. Reine Angew. Math. 138, 96-108, (1910).
VIJAYARAGHAVAN, T. On a theorem of J. L. Walsh concerning the moduli of zeros of polynomials. Proc.
Ind. Acad. Sci., Sect. A, 16, 83-86 (1942).
WARING, E. Meditationes algebraicae. Cambridge, 3rd ed. 1782, xliv + 403 p., p. 36-116.
WEBER, H. Lehrbuch der Algebra, Kleine Ausgabe. Braunschweig, vieweg, 1912, chap. 6, p. 135-154.
WEISNER, L. Moduli of the roots of polynomials and power series. Amer. Math; Month. 48, 33-36 (1941).
WEISNER, L. Polynomials whose roots lie in a sector. Amer. Jour. Math. 64, 55-60 (1942).
WEISNER, L. Roots of certain classes of polynomials. Bull. Amer. Math. Soc. 48, 283-286 (1942).
8. THE CALCULATION OF THE ZEROS OF A POLYNOMIAL
A. Iterative Methods (Newton-Raphson, False Position, etc.)
1918, p. 225-248.
CASALE, F. Su di una equazione collegata a quella di Keplero. I, II. Rend. 1st. Lombardo 72, 333-
346, 347-361 (1939).
DANDELIN, G. Recherches sur la resolution des equations rrameriques, Mem. Acad. Roy. Bruxelles 3,
v + 71 p., (1826).
DARBOUX, J. G. Sur la methode d 1 approximation de Newton. Nouv. Ann. Math. (2) 8, 17-27 (1869).
FABER, G. Uber die Newtonsche Naherungsformel. Jour. Reine Angew. Math. 138, 1-21 (191X3).
FABER- d. fiber die Newtonsche Naherunesformel (Zweite Abhandlune). Jour. Reine Angew. Math. 146.
229-233 (1916).
FOURET, G. Sur la methode d» approximation de Newton. Nouv. Ann. Math. (3) 9, 567-585 (1890).
FOURIER, J. B. J. Analyse des equations determinees. Premiere partie. Paris, Didot, 1830,
xxiv +258 p., p. 157-223.
HEYMANN, W. Theorie der An-und Umlaufe und Auflosung der Gleichungen vom vierten, funften und
sechsten Grade mittelst goniometrischer und hyperbolischer Functionen. Jour. Reine Angew.
Math. 113, 267-302 (1894).
HEYMANN, W. Ueber die elementare Auflosung transcendenter Gleichungen. Zeit. Math, Naturwiss.
Unterricht. 29, 1-15 (1898).
HEYMANN, W. Uber Wurzelgruppen, welche durch Umlaufe ausgeschnitten werden. Zeit. Math. Phys. 46,
265-297 (1901).
349
BIBLIOGRAFHY
HUBER, A. Uber Konvergenz-und Divergenzintervalle des Newtonschen Verfahrens. Sitzber. Akad. Wiss.
Wien. 134, 405-425 (1925).
ISENKRAHE, C. Ueber die Anwendung iterirter Functionen zur Darstellung der Wurzeln algebraischer
und transcendenter Gleichungen. Math. Ann. 31, 309-317 (1888).
LAGRANGE, J. L. De la resolution des equations numeriques de tous les degres. Paris, 1798, chap. 3.
LAGUERRE, E. Sur 1» approximation des fonctions circulaires au moyen des f onctions algebriques.
Oeuvres de Laguerre, vol. 1. Paris, Gauthier-Villars, 1898, p. 104-107.
LEGENDRE, A. M. Supplement a l'essai sur la theorie des nombres, seconde (1808) edition. Paris,
Courcier, 1816, p. 28-60.
s
LEMERAY, E. M. Sur le calcul des racines des equations par approximations successives. Nouv. Ann.
Math. (3) 17, 534-539 (1898).
LEVI, B. On the approximate solution of transcendental equations represented by Taylor series.
(Spanish). Math. Notae 3, 1-40 (1943).
LUROTH, J. Vorlesungen uber numerisches Rechnen. Leipzig, Teubner, 1900, 194 p.
MEHMKE, R. Neue Methode beliebige numerische Gleichungen mit einer Unbekannten graphische aufzulosen.
Ein Beitrag zum graphischen Rechnen. Civilingenieur (2) 35, 617-634 (1889) .
MEHMKE, R. Praktische Methode zur Berechnung der reellen Wurzeln reeller algebraischer oder trans-
cendenter numerischer Gleichungen mit einer Unbekannten. Zeit. Math. Phys. 36. 158-187
(1891).
NETTO, E. Ueber einen Algorithmus zur Auflosung numerischer algebraischer Gleichungen. Math. Ann.
29, 141-147 (1887).
NETTO, E. Vorlesungen uber Algebra. I. Leipzig, Teubner, 1896, p. 281-290.
NETTO, E. Elementare Algebra. Akademische Vorlesungen fur Studierende der ersten Semester. Arti-
cles 22, 45, 88. Leipzig, Teubner, 1904.
NEWTON, I. De analysi per aequationes nuraero terminorum infinitas: Cap. iv, Exempla per resolutionem
aequationum. In vol. 1 of Isaaci Newtoni opera quae exstant omnia, Samuel Horsley, ed.
London, J. Nichols, 1779, p. 268-270.
OSTROWSKI, A. ^ Sur la convergence et 1' estimation des erreurs dans quelques procedes de resolution
des equations. Memorial volume dedicated to D. A. Grave. Moscow, 1940, p. 213-234.
PASCAL, E. Repertorium der hoheren Mathematik. Vol. 1.(1). Leipzig, Teubner, 1910, p. 352-357.
PAWLET, M. G. New criteria for accuracy in approximating real roots by the Newton-Raphson method.
Nat. Math. Mag. 15, 111-120 (1940).
RAPHSON, J. Analysis aequationum universalis. London, 1690.
REHBOCK, F. Zur Konvergenz des Newtonschen Verfahrens fur Gleichungssysteme. Zeit. Aneew. Math
Mech. 22, 261-262 (1942).
RICHMOND, H. W. On certain formulae for numerical approximation. Jour.Lond.Math.Soc. 19, 31-38(1944).
RICHMOND, H. W. On the Newton-Raphson method of approximation. Edin. Math. Notes 34, 5-8 (1944) .
ROSS, R. A method of solving algebraic equations. Nature: 78, 663-665 (1908) j 79, 398-399 (1908).
RUNGE, C. Gleichungen. Separation und Approximation der Wurzeln. Ency. Math. Wiss.. LeiDzic
Teubner, 1899, I B 3a, p. 433-439, 446*448. '
RUNGE, C. and KONIG, H. Vorlesungen uber Numerisches Rechnen. Berlin, Springer, 1924, p. 152-157.
350
BIBLIOGRAPHY
SCARBOROUGH, J. B, Numerical Mathematical Analysis. Baltimore, Johns Hopkins Press, 1930, p. 178-195.
SCHEFFLER H* Auflosung der algebraischen Gleichungen. Braunschweig, 1359. Quoted from Eney. Math.
Wise. Vol. 1, p. 446.
SCRROEDER, E. Uber unendlich viele Algorithmen zur Auflosung der Gleichungen. Math. Ann. 2, 317-363
(1870).
SEIDEL, L. Uber ein Verfahren, die Gleichungen, auf welche die Methode der Kleinsten Quadrate
fiihrt, sowie lineare Gleichungen uberhaupt, durch successive Annaherung aufzuldsen. Abh.
Akad. Munchen 11, 81 (1874).
SMITH, D. E. History of Mathematics. Vol. 2: Special Topics of Elementary Mathematics. Boston, Ginn,
1925, p. 437-441.
TAUBER, A. fiber die Newton' sche Naherungsmethode. Monatsh. Math. Phys. 6, 291-302 (1895).
„,attto t t> -I--.W— +-„ „+«+„« « i^ift? «' mi . o <vP Wa lU a' f)p«i*A Mathematics. Oxford. 1695.
p. 381-398.
WAGNER, 1. Bestiooaing der Genauigkeit des Newton'sehen Verfahrens. Berlin, (Latin, 1855; German,
2*£qV Qiigfraj? from Esey* Math s Wis®* Vol* .1, p* 434?
WARD, G. W. Successive approximations to \j~*l Math. Gaz. 17, 52-53, 127 (1933).
WHTTTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow and London, Blackie, 1942,
p. 94-95.
B. Root-Squaring and Allied Methods
BAIRSTOW, L. Applied Aerodynamics. New York, Longmans, 1920, p. 551-560.
p muuu PlfU T ~— J Oimo f!. Vr*r*1 ammtram uKai* A 1 MiHra . R»i»Hn. Tsilhnai*- 1928. T>. 17L/-3U7 .
ir i ni *■•■' ' i '"*!'", jj. oaj-- • — - --- ■ — - '- - - ■ - -
BR0DETSKY, S. and SMEAL, G. On Graeffe's method for complex roots of algebraic equations. Proc.Camb,
Phil. Soc. 22, 83-87 (1924).
CARVALLO, M. E. Methode pratique pour la resolution numerique complete des equations algebriques
ou transcendantes. Paris, Nony, 1896, 32 p.
>, «*« \— ■-
BANDELIN, S. 3ur la resolution des equations nuissriques . Mesi. Acad. Roy. Br
ENCKE, J. F. Allgemeine Auflosung der numerischen Gleichungen. Jour. Reine Angew. Math. 22,193-
248 (ISO).
GRAFFE, C. H. Die Auflosung der hoheren numerischen Gleichungen... Zurich, Schulthess, 1837, 34 p.
LEVI, D. On the approximate solution of transcendental equations represented by Taylor series. Math.
Notae 3, 1-h40 (1943).
OSTROWSKI, A. Recherches sur la methode de Graeffe et les zeros des polynomes et des series de
Laurent. I-IV. Acta Math. 72, 99-257 (1940).
RUNGE, C. Gleichungen. Separation und Approximation der Wurzeln. Ency. Math. Wiss. Leipzig,
Teubner, 1899, I B 3a, section 14, p. 440-446.
RUNGE, C. and K0NIG, H. Vorlesungen uber numerisches Rechnen. Berlin, Springer, 1924, p. 164-175*
RUNGE, C. Praxis der Gleichungen. Berlin, de Gruyter, 2nd ed. 1921, 172 p.
351
BIBLIOGRAPHY
SAN JUAN, R. Complements to Graeffe's method for the solution of algebraic equations. Revista Mat.
Hisp.-Amer. (3) 1, 1-14 (1939).
SCARBOROUGH, J. B. Numerical Mathematical Analysis. Baltimore, Johns Hopkins Press, 1930, chap. X.
SEBASTIAO e SUVA, J* Sur une methode d' approximation semblable a celle de Graeffe. Portugaliae
Math. 2, 271-279 (1941).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 3rd ed. 1942,p.
106-119.
C. Miscellaneous Methods.
AITKEN, A. C. On Bernoulli's numerical solution of algebraic equations. Proc. Roy. Soc. Edin. 46,
289-305 (1926).
BERNOULLI, D. Observationes de seriebus quae formantur ex additione vel subtractions quaecunque
terminorum se mutuo consequentum, ubi praesertim earundem insignis usus pro inveniendis
radicum omnium aequationum algebraicarum ostenditur. Comment. Acad. Sci. Petropol. 3, 85-
100 (1732).
COHN, F. Ueber die in recurrirender Weise gebildeten Grossen und ihren Zusammenhang mit den algebra-
ischen Gleichungen. Math. Ann. 44, 473-538 (1894).
COLLATZ, L. Das Hornersche Schema bei komplexen Durzeln algebraischer Gleichungen. Zeit. Angew.
Math. Mech. 20, 235-236 (1940).
CORNOCK, A. F. and HUGHES, J. M. The evaluation of the complex roots of algebraic equations. Phil.
Kag. (7) 34, 314-320 (1943).
EAGLE, A. Series for all the roots of a trinomial equation. Amer. Math. Month. 46, 422-425 (1939) .
EICHLER, M. Zur numerischen Losung von Gleichungen mit reellen Koeffizienten. Jour. Reine Angew.
Math. 184, 124-128 (1942).
EULER, L. Introductio in analysin infinitorum. Lausanne, Bosquet, 1748, xvi +- 320 p., chap. 17.
FOURIER, J. B. J. Analyse des equations de'terminees. Paris, Didot, 1830, xxiv + 258 p., p. 68-86.
FRAZER, R. A., DUNCAN, ff. J. and COLLAR, A. R. Elementary Matrices and Some Applications to Dynamics
and Differential Equations. Cambridge, Cambridge Univ. Press, 1938, p. 148-151.
n
FURSTENAU. Darstellung der reellen Wurzeln algebraischer Gleichungen durch Deterndnanten der Coef-
ficienten. Marburg, 1860. Quoted from Aitken, A. C, Proc. Roy. Soc. Edin. 46,1926, p. 303.
HITCHCOCK, F. L. Algebraic equations with complex coefficients. Jour. Math. Phys. (M.I.T.) 18,202-
210 (1939).
HITCHCOCK, F. L. An improvement on the G.C.D. method for complex roots. Jour. Math. Phys. (M.I.T.)
23, 69-74 (1944).
HORNER, W. G. A new method of solving numerical equations of all orders, by continuous approxi-
mation. Phil. Trans. Roy. Soc. London 109 Part 2, 308-335 (1819)j also Ladies Diary 135,
49-72 (1838).
HORNER, W. G. On the popular methods of approximation. Math. Repository. New Series. 4 Part 2. 131-
136 (1819).
HORNER, W. G. Horae mathematicae. Math. Repository, New Series, 5 Part 2, 21-75 (1830) .
JACOBI, C. J. G. Observatiunculae ad theoriam aequationum pertinentes. V. Quomodo regula Ber-
noulliana ad investigandas radices, quae maximam aut mjn-tmani sequuntur, extendi potest.
Jour. Reine Angew. Math. 13, 349-353 (1835) .
352
BIBLIOGRAPHY
KEMPNER. A. J. On the complex roots of algebraic equations. Bull. Amer. Math. Soc. 41, 809-843
(1935).
KONIG, J. Ueber eine Eigenschaft der Potenzreihen. Math. Ann. 23, 447-449 (1884).
KRAFFT, M. Uber ein Eulersches Verfahren zur Wurzelberechnung. Monatsh. Math. Phys. 49, 312-315
(1941).
LAGRANGE, J. L. De la resolution des equations numeriques de tous les degre's. Paris, Duprat, 1798
chap. 3*
LAGUERRE, E. Sur une methode pour obtenir par approximation les racines d'une ^J?" J^§f^ e
uuhiuu, ^ ^ ^^ ses racines replies. Oeuvres de Laguerre, vol. 1. Paris, Gauthier-Villars,
1898, p. 87-103.
LEWIS, A. J. The solution of algebraic equations by infinite series. Nat. Math. Mag. 10, 80-95
(1935).
LIN, SHIH-NGE. A method of successive approximations of evaluating the real and complex roots of
cubic and higher-order equations. Jour. Math. Phys. (M.I.T. } 20, 231-242 U941J.
ttk ctsTO^Msw * *«rf-fcrw* f<w» **ndiRff roots of alsebraic eauations, Jour e Math, Phys. (M.I.T.) 22.
60-77 (1943).
NAEGELSBACH H. Studien zu Furstenau«s neuer Methode der Darstellung und Berechnung der Wurzeln
algebraischer Gleichungen durch Determinant en der Coefficienten. Archiv Math. Phys.: 59,
147-192 (1876) j 61, 19-85 (1877).
NIEWENGLOWSKI B. Coars d'algebre. Paris, Armand Colin, vol. 2, 7th ed. 1916, 570 p., p. 417-458.
PERRON, 0. Algebra. Berlin, de Gruyter, vol. 2, 2nd ed. 1933, viii + 260 p., p. 47-56.
RDNGE C. Gleichungen. Separation und Approximation der Worseln. Ency. Math* W±ss. Leipzig,
* Teubner, 1899, I B 3a, p. 439-440.
SHARP K. S. A caparison of set-hods for evaluating the complex roots of quartic equations. Jour.
«u~-, «. -.^ -—^ (mT.T.) 20, 243-258 (1941).
STERN M. A. Theorie der Kettenbruche und ihre Anwendung. Jour. Reine Anger. Math. U, 142-168,
277-306 (1834).
VINCENT M. Note sur la resolution des equations numeriques. Jour. Math. Pures Appl. 1, 341-372
(1836).
WEIL, H. Randbemerkungen zu Hauptproblemen der Mathematik. Math. Zeit. 20, 130-150, espec. 142-146
(1924).
WIENER A. Die Berechnung der reellen lifurzeln der quartinomischen Gleichungen. Zeit. Math. Phys.
31. 65-87 (1886).
YOUNG, J. R. On the Theory and Solution of Algebraical Equations. London, Souter, 1st ed. 1835,
xviii + 271 p.
9. THE ZEROS OF TRANSCENDENTAL EQUATIONS
A. Iterative Methods (see also under 8A)
BOURLET, C. Sur le problems de I 1 iteration. Ann. Toulouse 12, C 1-12 (1898).
CAUGHT, A. L. Analyse algebrique. Note III. See Oeuvres completes d*Augustin Cauchy, 2nd series,
vol. 3. Paris, Gauthier-Villars, 1897, p. 381-386.
353
BIBLIOGRAPHY
DART, M. Letter to Newton (August 1674)* See Rigaud, S, P. and S. J., Correspondence of Scientific
Men of the Seventeenth Century (Earl of Macclesfield Collection). Oxford, Oxford Univ.
Press, 1841, vol. 2, 365-367.
DeMORGAN, A. Treatise on the Calculus of Functions* (Extracted from the Encyclopedia Metropolitana.)
London, Baldwin and Cradock, 1$36, BB p.
DeMORGAN, A. Encyclopaedia Metropolitana. 1845, vol. 2, p. 305-389.
FOURIER, J. B. J. Thebrie analytique de la chaleur. Paris, Didot, 1822, xxii + 639 p., P. 342-346.
FOURIER, J. B. J. Analyse des equations determiners. Paris, Didot, 1830, xxiv + 258 p., p. 41*
FARKAS, J. Sur les fonctions iteratives. Jour. Math. Pures Appl. 10, 101-108 (1884).
GERMANSKY, B. Notiz uber die Losung von Extremalaufgaben mittels Iteration. Zeit. Angew. Math. Mech.
14, 187 (1934).
GREGORY, J. Letter to Collins (April 1674). See Rigaud, S. P. and S. J., Correspondence of Scientific
Men of the Seventeenth Century (Earl of Macclesfield Collection) . Oxford, Oxford Univ.
Press, 1841, vol. 2, p. 255-256.
HALL, N. A. The solution of the trinomial equation in infinite series by the method of iteration.
Nat. Math. Mag. 15, 1-11 (1941).
n n
HEYMANN, W. Uber die elementare Auflosung transcendenter Gleichungen. Zeit. Math. Natumiss.
Unterricht 29, 1-15 (1898).
ISENKRAHE, C. uber die Anwendung iterirter Functionen zur Darstellung der Wurzeln algebraischer
und transcendenter Gleichungen. Math. Ann. 31, 309-317 (1888).
ISENKRAHE, C. Das Verfahren der Functionswiederholung, seine geometrische Veranschaulichung und
algebraische Anwendung. Wissenschaftliche Beilage zum Jahresbericht des Kgl.Kaiser-Wilhelm-
Gymnasiums in Trier. 1897, viii + 113 p.
JULIA, G. Memoire sur la convergence des series formees avec les iterees successives d'une fraction
rationelle. Acta Math. 56, 149-195 (1930).
KING, L. V. On the Direct Numerical Calculation of Elliptic Functions and Integrals. Cambridge,
Cambridge Univ. Press, 1924, viii +■ 42 p.
KOENIGS, G. P. Recherches sur les substitutions uniformes. Bull. Sci. Math. (2) 7 (1). 340-357
(1883).
LEGENDRE, A. M. Supplement a 1'essai sur la thebrie des nombres, seconde (1808) edition. Paris,
Courcier, 1816, p. 28-37.
LEMERAY, E. M. Sur la convergence des substitutions uniformes. Nouv. Ann. Math.: (3) 16, 306-319
(1897); (3) 17, 75-80 (1898).
LEMERAY, E. M. Sur quelques algorithmes et sur 1» iteration. Bull. Soc. Math. France 26, 10-15 (1898).
VON MISES, R. and POLLACZEK-GEIRINGER, H. Praktische Verfahren der Gleichungsauflosung. I. Zeit.
Angew. Math. Mech. 9, 58-62 (1929).
MONTEL, P. L'lteration. Univ. Nac. La Plata Publ. Fac. Ci. Fisicomat. Revista (2) 3, 201-211 (1940).
NETTO, E. Vorlesungen uber Algebra. Leipzig, Teubner, 1896, vol. 1, p. 300-323.
PELLET, A. Calcul des racines reelles d'une equation. C. R. Acad. Sci. Paris 133, 917-918, 1186-
1187 (1901).
PERRIN, S. Sur la separation et le calcul des racines replies des equations. C. R. Acad. Sci. Paris
133, 1189-1191 (1901).
354
BIBLIOGRAPHY
PIHCHERLB. S. Equations fonctionelles. Ency. Sci. Math. II 5 (1) 55-72 (1912).
RUNGE, C. and KONIG, H. Vorlesungen uber Numerisches Rechnen. Berlin, Springer, 1924, p. 155=157.
SANCERY, L. De la methode des substitutions successive8 pour le calcul des racines des equations.
Nouv. Ann. Math. (2) 1, 305-312 (1862).
SCARBOROUGH, J. B. Numerical Mathematical Analysis e Baltimore, Johns Hopkins Press, 1930, p. 184-
187, 191-195.
SCHROEDER, E. Ueber unendlich viele Algorithmen zur Auflosung der Gleichungen. Math.Ann. 2, 317-365
(1870).
SIEGEL, C, L. Iteration of analytic functions. Ann, of Math, (2) 43, 607-612 (1942).
SPOERL, C. A. Solving equations in the machine age. Record Amer. Inst. Actuar. 31, 129-149, 490-
506 (1942).
VALIRON, G. Sur 1'iteration des fonctions holomorphes dans un dend-plan. Bull. Sci. Math. (2) 55,
105-128 (1931).
B. Miscellaneous Methods
AUGE, J. On the zeros of polynomials and Laurent series. (Spanish). Revista Mat. Hisp.-Amer. (4) 3,
176-185, 229-241 (1943).
BLEICK, W. E. Symmetric relations between the coefficients of reversed power series. Phil. Mag. (7)
33, 637-^38 (1942).
BUEKHARDT, K. Trigonometrische Reihen und Integrale bis etwa 1850: Darsteiiung der mirzeln von
Gleichungen durch Integrale. Ency. Math. Wiss., Leipzig, Teubner, 1915, II 1 (2) p. 1307-
1311.
CAUCHY, A. L. Lecons sur le calcul differentiel. Note: sur la determination approximative des
racines... Oeuvres completes d'Augustin Cauchy, (2) vol. 4. Paris, Gauthier-Villars, 1899,
p. 573-609.
COHN F. Ueber die in recurrirender Weise gebildeten Grossen und ihren Zusammenhang mit den
algebraischen Gleichungen. Math. Ann. 44, 473-538 (1894).
CURRY, K. B. The method of steepest descent for non-linear adniaiaation problems. Quart, Appl* Math,
2, 258-261 (1944).
BEHN, M. and HELLINGER, E. On James Gregory's Vera Quadratura. The James Gregory Tercentenary
Memorial Volume. London, Beii, 1939, p. 468-478.
EULER, L. Introductio in analysin infinitorum, tomus primus. Lausanne, Bosquet, 1748, xvi + 320 p.,
section 355, p. 294-295.
EULER,L. De radicibis aequationis infinitae, = 1-xx/ n(n+l)-t-xV n(n+l)(n+2)(n+3) -x / n...(n+5) +
... etc. Nova Acta Acad. Sci. Petropol. 9, 19-40 (1791).
FUJIWARA, M. On the zero points of integral transcendental functions of finite genus. Jap. Jour.
' Math. 1, 27-28 (1924).
FUJIHARA, M. Uber die Nullstellen der ganzen Funktionen vom Geschlecht Null und Eins. T&hoku Math.
' Jour. 25, 27-35 (1925).
GERCEVANOFF, N. Quelques proce'des de la resolution des equations fonctionelles lineaires par la
me'thode d'iteration. C. R. (Doklady) Acad. Sci. URSS (N.S.) 39, 207-209 (1943).
355
BIBLIOGRAPHY
GOLOMB, H. Zeros and poles of functions defined by Taylor series. Bull. Amer. Math. Soc. 49, 581-592
(1943).
HILLMAN, A. P. and SALZER, H. E. Roots of sin z - z. Phil. Mag. (7) 34, 575 (1943).
ii
HURWITZ, A. Uber die Iffurzeln einiger transcendenten Gleichungen. Mitt. Math. Ges. Hamburg 2. 25-31
(1890).
n
LEHMANN, A. Uber die Inversion des Gaussschen Wahrscheinlichkeits-Integrals. Mitt. Verein Schweiz.
Versich. Math. 38, 15-52 (1939).
LEVI, B. On the approximate solution of transcendental equations represented by Taylor series.
(Spanish). Math. Notae 3, 1-40 (1943).
MEYER, F. Zur Auflosung der Gleichungen. Math. Ann. 33, 511-524 (1889).
PLDMMER, H. C. The numerical solution of a type of equation. Phil. Mag. (7) 32, 505-512 (1941).
POLYA, G. Uber das Graeffesche Verfahren. Zeit. Math. Phys. 63, 275-290 (1914).
PONTRJAGIN, L. On zeros of some transcendental functions. (Russian. English summary.). Bull. Acad.
Sci. URSS. Ser. Math. (Izvestia Akad. Nauk SSSR) 6, 115-134 (1942).
RUNGE, C. Entwicklung der Wurzeln einer algebraischen Gleichung in Summen von rationalen Functionen
der Coefficienten. Acta Math. 6, 305-318 (1885).
SCHROEDER, E. Ueber unendlich viele Algorithmen zur Auflosung der Gleichungen. Math. Ann. 2. 317-
365 (1870).
STERN, M. A. Ueber die Auflosung der transcendenten Gleichungen. Jour. Reine Angew. Math. 22, 1-62
(1841).
«
TCHEBOTAROW, N. On the methods of Sturm and Fourier for transcendent functions. C. R. (Doklady)
Acad. Sci. URSS (N.S.) 34, 2-4 (1942).
TCHEBOTAROW, N. On a particular type of transcendent equations. C. R. (Doklady) Acad. Sci. URSS
(N.S.) 34, 38-41 (1942).
TCHEBOTAR&W, N. On entire functions with real interlacing roots. C. R. (Doklady) Acad. Sci. URSS
(N.S.) 35, 195-197 (1942).
WHITTAKER, e. T. A formula for the solution of algebraic or transcendental equations. Proc. Edin.
Math. Soc. 36, 103-106 (1918).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 3rd. ed. 1942,
p. 120-123.
10. IMPLICIT FUNCTIONS
BIEBERBACH, L. Lehrbuch der Funktionentheorie, vol. I. Leipzig, Teubner, 3rd ed. 1930, p. 195-204.
COPSON, E. T. Introduction to the Theory of Functions of a Complex Variable. Oxford. Oxford Univ.
Press, 1935, p. 121-125.
EAGLE, A. Series for all the roots of the equation (z - a) m = k(z - b) n . Amer. Math. Month. 46.
425-428 (1939).
EAGLE, A. Series for all the roots of a trinomial equation. Amer. Math. Month. 46, 422-425 (1939).
HURWITZ, A. and COURANT, R. Vorlesungen uber Allgemeine Funktionentheorie und elliptische Funktionen.
Berlin, Springer, 1929, xii + 534 p.
356
BIBLIOGRAPHY
"*
_.__.—__ - * <t ti 'i.% j_ -v_™ „«^^i^-w.« iae « rn .?t-io"« T4+t«'*o' , e* nar To iBnTOti des series*
« „ ,*» T»^,„«»« ir«1 . •?. Pj»yHs. f*j»»+.M*n>Jttt liars. 1869. r>. 1-73.
PFAFF J. F. Disquisitiones analyticae maxime ad calculum integralem et doctrinam serierum per-
' tinentes, vol. 1, sect. 2. Third paper: Tractatus de reversione serierum, sive de reso-
lutione aeqaationum per series. Relmstedt, Fleckeisen, 1797, 350 p., p. 227-350.
PINCHERLE, S. Gli element! della teoria delle funzioni analitiche. 1922, p. 239 ff j p. 213.
SCHLOEMILCH, 0. Die allgemeine Umkehrung gegebener Funktionen. Halle, H. W. Schmidt, 1849, 56 p.
WHITTAKER, E. T. and WATSON, G. N. Modern Analysis. New York, Macmillan, Amer. ed. 1943, p. 128-133.
11. HARMONIC ANALYSIS
BERGER, E. R. Harmonische Analyse diskreter Zahlenreihen. Zeit. Angew. Math. Mech. 22, 269-272
(1942).
BRUNT, D. The Combination of Observations. Cambridge, Cambridge Univ. Press, 2nd ed. 1931, x ■+■ 239
p., chap. XI, p. 179-205.
CARSE, G. A. and SHEARER, G. A Course in Fourier^ Analysis and Periodogram Analysis for the Math-
ematical Laboratory. Edin. Math. Tracts, No. 4. London, Bell, 1915, viii + 66 p.
CONRAD, V. Zur Berechnung hoherer Glieder der Fourierschen Reihen. Meteorol. Zeit. 36, 160 (1919).
DALE, J. B. The resolution of a compound periodic function into simple periodic functions .Month.
Notices Roy. Astr. Soc. 74, 628-648 (1914).
DANIELSON, G. C. and LANCZ0S, C. Some improvements in practical Fourier analysis and their appli-
cation to X-ray scattering from liquids. Jour. Franklin Inst. 233, 365-380, 435-452 (1942).
DIETSCH, G. and R0TZEIG, B. Eine neue Methode zur exakten Berechnung der Fourierkoeffizienten.
Beitrage zur Geophysik (Gerlands Beitrage) 38, 276-281 (1933) .
EAGLE, A. A practical Treatise on Fourier«s Theorem and Harmonic Analysis: for Physicists and Engi-
neers. London, Longmans Green, 1925, xiv + 178 p.
ESPLEY, D. C. Harmonic analysis by the method of central differences. Phil. Mag. (7) 28, 338-352
(1939).
FISCHER-HINNEN, J. Methode zur schnellen Bestimmung harmonischer Wellen.Elektrotech. Zeit. 22, 396-
398 (1901).
LAGRANGE, J. L. Recherches sur la maniere de former des tables des planetes d'aprfcs les seules
_t~_.£ *4 n— , « >»« t »_.,»,«» „«i A Don^ rr«,,+>,-««T._TM-noi.«> istrrt -n «ai«c_A99 .
LAGRANGE, J. L. Sur les interpolations. Oeuvres de Lagrange, vol. 7. Paris, 1877, p. 533-553.
LINCOLN, P. M. Wave form analysis. The Electric Jour. (Publ. by The Electric Club, Pittsburg, Pa.)
5, 386-392 (1908).
LIPKA, J. Graphical and Mechanical Computation. New York, Wiley, 1918, p. 170-208.
L0WAN, A. N. and LADERMAN, J. Table of Fourier coefficients. Jour. Math. Phys. (M.I.T.) 22, 136-
147 (1943).
P0LLAK, L. W. Rechentafeln zur Harmonischen Analyse. Leipzig, Barth, 1926, 22 p. text and 138 p.
tables.
ROSS, M. A. S. Numerical Fourier analysis to twenty-nine harmonics. Nature 152, 302-303 (1943).
357
BIBLIOGRAPHY
RUHGE, C. Uber die Zerlegung empirischgegebener periodischer Punktionen in Sinuswellen. Zeit. Math.
Phys. 48, 443-456 (1903).
n
RUNGE, C. Uber die Zerlegung einer empirischen Funktion in Sinuswellen. Zeit. Math. Phys. 52, 117-
123 (1905).
RUNGE, C. and EMDE, F. Rechnungsfonaular zur Zerlegung einer empirisch gegebenen periodischen
Funktion in Sinuswellen. Braunschweig, Vieweg, 1913.
RUSSELL, A. Practical harmonical analysis. Proc. Phys. Soc. Lond. 27, 149-170 (1915).
SCHLAEFKE, K. Zur hannonischen Analyse von Nockenkurven. Luftfahrtforschung 17, 87-88 (1940) .
STUMPFF, K. Grundlagen und Methoden der Periodenforschung. Berlin, Springer, 1937, viii + 332 p.
STUMPFF, K. Tafeln und Aufgaben zur hannonischen Analyse und Periodogramrarechnung. Berlin- Springer,
1939, Til + 174 p.
TAILOR, H. 0. A mechanical process for constructing harmonic analysis schedules for waves having
even and odd harmonics. Phys. Rev. (2) 6, 303-311 (1915).
THOMPSON, S. P. Note on a rapid approximate method of harmonic analysis. Proc. Phys. Soc. Lond. 19.
443-450 (1905).
THOMPSON, S. P. ^ Nouvelle methode d» analyse harmonique par la sommation algebrique d'ordonnees de~
terminees. C. R. Acad. Sci. Paris 153, 88-90 (1911).
THOMPSON, S. P. A new method of approximate harmonic analysis by selected ordinates. Proc. Phys.
Soc. Lond. 23, 334-343 (1911).
TURNER, H. H. The facility of harmonic analysis. Jour. Brit. Astr. Assoc. 18, 250-254 (1908).
TURNER, H. H. Tables for facilitating the use of harmonic analysis. London, Humphrey Milford, 1913,
46 p.
ZECH, T. Harmonische Analyse mit Hilfe des Lochkartenverfahrens. Zeit. Angew. Math. Mech. 9. 425-
427 (1929).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. London, Blackie, 3rd ed. 1942. r>.
260-284.
12. PERIODOGRAM ANALYSIS
ALTER, D. Application of Schuster's periodogram to long rainfall records, beginning 1748. Month.
Weather Rev. 52, 479-487 (1924).
ALTER, D. An examination by means of Schuster 1 s periodogram of rainfall data from long records in
typical sections of the world. Month. Weather Rev. 54, 44-56 (1926) .
ALTER, D. The criteria of reality in the periodogram. Month. Weather Rev. 54, 57-58 (1926).
ALTER, D. An extremely simple method of periodogram analysis. Proc. Nat. Acad.Sci. U.S A 19 335-
339 (1933). '
BARTELS, J. Random fluctuations, persistence, and quasi-persistence in geophysical and cosmical
periodicities. Terr. Magnetism 40, 1-60 (1935) .
BERNSTEIN, F. Uber die arithmetischer Ermittlung verborgener Periodizitaten. Zeit. Aneew. Math
Mech. 7, 441-444 (1927).
BERNSTEIN, N. Analyse aperiodischer trigonometrischer Reihen. Zeit. Angew. Math. Mech. 7. 476-485
(1927) .
358
BIBLIOGRAPHY
BROOK - C. b. P. The difference-periodogram— a method for the rapid determination of short periodic-
' "ities. Proc. Roy. Soc." Lond. A105, 346-359 (1924).
BRUNT, D. Periodicities in European Weather. Phil. Trans. Roy. Soc. Lond. A225, 247-302 (1925).
See also An investigation of periodicities. Quart. Jour. Roy. Met. Soc. 53, 1-29 (1927).
BRUNT, D. The Combination of Observations. Cambridge, Cambridge Univ. Press, 2nd ed. 1931, x + 239
p., chap. XII, p. 206-231.
BRUNT, D. Harmonic analysis and the interpretation of the results of periodogram-investigations.
Mem. Roy. Met. Soc. 2, No. 15, 48-68 (1928).
CARSE, G. A. and SHEARER, G. A Course in Fourier's Analysis and Periodogram Analysis for the Math-
ematical Laboratory, Edin. Math. Tracts No. 4. London, Bell, 1915* viii + 66 p.
CONRAD, V. Der Expektanzbegriff von Arthur Schuster. Meteorol. Zeit. 59, 299-306, 389-390 (1924).
i-itotj r> mi ___i-^I„™«-, « m «1^-<,4o «•*> +Vn» mn^sHnna nf SS r.vtmi . Urm+.h - Notifies Rov. Astr. SOC. 74.
it i ririj u» J.ll'C ^QlAUUVglBuu oi»*j wiw wa t#uw v««a^.%- •»«.%*««» w* —a- ~^ — • . „ - - - - . .,
678-686 (1914).
HIRAIAMA, S. Note on the method to find the period of a periodic function from equidistant- obser-
va *. / « nna _ t^_~- ., fokves Math- Phvs. Sec. (2} 7. 268—274 (1916).
HOLTZHEI-LINDAU, R. Eine Ausgleichungsbetrachtung. Zeit. Angew. Met. 48, 83-91 (1931).
KELLER, L. Die Periodographie als Statistisches Problem. Beitr. Physik frei Atmosph. 19, 173-187
(1932).
KELLEI, T. L. The evidence for periodicity in short time series. Jour. Amer. Statist. Assoc. 38,
319-326 (1943).
KRASSOWSKI, J. Analyse, au moyen de la methode de M. Schuster, des periodes de la variation de la
latitude. Bull. Internat. Acad. Sci. Cracovie, CI. Sci. Math. Nat. 1909, 543-548 (1909).
LABROUSTE, H. Analyse des courbes re'sultant de la superposition de sinuso'ides. C. R. Acad. Sci. Paris
184, 259-261 (1927).
VON LAUE, M. Ein Satz der "ffahrscheinlichkeitsrechnung und seine Anwendung auf die Strahlungstheorie.
Ann. der Phys. (4) 47, 853-878 (1915)*
McNISH A. G. Principles of statistical analysis occasionally overlooked. Jour. Franklin Inst. 215
' 697-703 (1933).
MUNZNER, H. Gunstigste Bestimmung der Umkehrung der Laplace-Transformierten zur Auffindung Ver-
borgener Periodizitaten. Dissertation, Gottingen, 1932, 45 p.
REINSBERG, C. Beitrage zur Theorie der Aufsuchung versteckter Periodizitaten. Astr. Nachr, 248,
REINSBERG, C. Zur Theorie der Expoiieiitialper-iodograaauo. Astr. Nachr. 252, 33<->— 34<j v!934/«
RIETZ, H. L. and BAUR, F. Handbuch der Mathematischen Statistik. Leipzig, Teubner, 1930, vi + 285 p.
RUSSELL, A. Practical harmonical analysis. Proc. Phys. Soc. Lond. 27, 149-168 (1915).
SAVUR, S. R. A simplified method for calculating periodicities. Proc. Ind. Assoc. Sci. 6, 527-
541 (1931).
SCHUSTER, A. On lunar and solar periodicities of earthquakes. Proc .Roy. Soc. Lond. 61, 455-^65 (1897).
SCHUSTER, A. The investigation of hidden periodicities. Terr. Magnetism 3, 13-41 (1898).
SCHUSTER A* The ■ n eriodo« T rasi of jsa'^netic declination as obtained from the records of the Greenwich
Observatory during the years 1871-1895. Trans. Camb. Phil. Soc. 18, 107-135 (1900).
359
BIBLIOGRAPHY
SCHUSTER, A, The periodogram and its optical analogy. Proc. Roy. Soc. Lond. A77, 136-140 (1906).
SCHUSTER, A. On the periodicities of sun spots. Phil. Trans. Roy. Soc. Lond. A206, 69-100 (1906).
STERNE, T. E. and CAMPBELL, L. Properties of the light-curve of "t^ - Cygni. Ann. Harvard Coll.
Obs. 90, No. 6, 189-206 (1934). d d
STUMPFF, K. Tafeln und Aufgaben zur hannonischen Analyse und Periodogrammrechnung. Berlin, Springer.
1939, vii+174 p.
STUMPFF, K. Grundlagen und Methoden der Periodenf orschung. Berlin, Springer, 1937, vii +■ 332 p.
TURNER, H. H. Tables for Facilitating the Use of Harmonic Analysis. Oxford, Oxford Univ. Press.
1913, 46 p. *
TURNER, H. H. On double lines in periodograms. Proc. 5 Internat. Math. Congr. vol. 2. Cambridge.
Cambridge Univ. Press, 1913, p. 177-181.
WALKER, G. T. On periodicity. Quart. Jour. Roy. Met. Soc. 51, 337-346 (1925).
WALKER, G. T. On periodicity and its existence in European weather. Mem. Roy. Met. Soc. 1. No. 9
119-126 (1927). '
WALKER, G. T. On periodicity iii. Criteria for reality. Mem. Roy. Met. Soc. 3, No. 25, 97-101(1930).
WALKER, G. T. On periodicity in series of related terms. Proc. Roy. Soc. Lond. A131, 518-532 (1931).
WORTHING, A. G. and GEFFNER, J. Treatment of Experimental Data. New York, ?/iley, 1943, iv -+- 342 p.
13. FINITE DIFFERENCES
ABRAMOWITZ, M. Note on the computation of the differences of the Si(x), Ci(x), Ei(x) and -Ei(-x)
functions. Bull. Amer. Math. Soc. 46, 332-333 (1940).
ADAMS, C. R. Bibliography, supplementary to Norlund's bibliography on the calculus of finite differ-
ences and difference equations. Bull. Amer. Math. Soc. 37, 383-400 (1931).
ANDOYER, H. Calcul des differences et interpolation. Vol. I, part 21 in 1(4) fasc. 1 of Ency. des
Sci. Math., 1906, p. 47-160.
BENNETT, H. F. Computation of polynomial functions by summation of finite differences. Jour. 0t>t
Soc. Amer. 33, 519-526 (1943).
BEZ0UT, E. Thebrie ge'herale des equations algebriques. Paris, P. D. Pierres, 1779, xxviii + 471 p.
p. 1—19.
BLEICH, F. and MELAN, E. Die gewohnlichen und partiellen Differenzengleichungen der Baustatik.
Berlin, Springer, 1927. Chap. 1, p. 1-34.
BOOLE, G. A Treatise on the Calculus of Finite Differences. London, Macmillan, 3rd ed. J. F. Moulton
1880. Reprinted New York, Stechert, 1931, xii + 336 p. "uuiwn
B0SSUT, C. Difference. Encyclopedic methodique, mathematiques. Paris, 1, 512-520 (1789).
BRIGGS, H. Trigonometria Britannica: sive De doctrina triangulorum libri duo. Gouda, Rammasenius.
1633, 110 p., liber primus, cap. xii, p. 35-40. '
BURN, J. and BROWN, E. H. Elements of Finite Differences... London, Layton, 2nd ed. 1915, 289 p. p.
CARMICHAEL, R. A Treatise on the Calculus of Operations: Designed to facilitate the processes of
Ssf lS^r^ +%^!!^! 137-lSr Snd ^ ° alCUlUS ° f Flnite Wfferences - London,Long-
360
BIBLIOGRAPHY
CA30HATI F. II calcolo delle differense finite interpretato ed aecresciuto di nuovi teoremi a
' sussidio princ-ipaliBanta delle odierne ricerche basate sulla variability complessa. Ann.Mat.
Pura Appl? (2) 10, 10-43 (1880-1882).
COTES, R. Canonotechnica sive Construotio tabularum per differentias. See Opera Miscellanea Rogerl
Cotes. Cambridge, 1722, 125 p., p. 35-71 (Publ. with but paged separately from Harmonia
mensurarum.).
DellORGAN, A. The Differential and Integral Calculus. London, Baldwin, 1842, xx + 849 p., P. 77-85,
253-266.
DZIOBEK, 0. Vorlesungen uber Differential-und Integralrechnung. Leipzig, Teubner, 1910, x + 648 p.
EMERSON, W. The Method of Increments. London, J. Nourse, 1763, viii + 147 p.
ENCKE, J. F. Ueber mechanische Quadratur. See Gesammelte mathematische und astronomische Abhandlungen
von J. F. Encke, vol. 1. Berlin, Dummler, 1888, 211 p., p. 21-60.
EDLER, L. Institutiones calculi differentialis. St. Petersbourg (Leningrad), 1755, xxiv + 880 p.
FORSYTH, C. H. An Introduction to the Mathematical Analysis of Statistics. New York, Wiley, 1924,
vii + 241 p., chap. 2, p. 12-32.
GAU E. P. Calculs numeriques et graphiques. (Coll. Armand Colin, No. 60) Paris, Colin, 1925, 206 p.
GIBB, D. A Course in Interpolation and Numerical Integation for the Mathematical Laboratory. Edin.
Math. Tracts No. 2. London, Bell, 1915, viii + 90 p.
GRANT, J. D. Notes on the Calculus of Finite Differences. Ann Arbor, Edwards Bros., 1926, 94 P.
mimeo.
HANSEN, P. A, Relatione^ einestheils zwischen Suramen und Differenzen und anderntheils zwischen
Integralen und Differentialen. Abh. Ges. Wiss. Leipzig 7, 506-583 (1865).
HERSCHEL, J. F. W. A Collection of Examples of the Applications of the Calculus of Finite Differ-
ences. Cambridge, Deighton, 1S20, v + 171 p.
HYMERS, J, A Treatise on Differential Equations and on the Calculus of Finite Differences. London,
Longmans, 2nd ed. 1858, viii + 318 p., second treatise, 139 p.
JARRET, T. An Essay on Algebraic Development... and in the Calculus of Finite Differences. Cambridge,
Deighton, 1831, iv +192 p., p. 40-65.
JOLLEY, L. B. W. Summation of Series. London, Chapman and Hall, 1925, xi + 232 p.
JORDAN, C. Statistique Mathematique. Paris, Gauthier-Villars, 1927, xvii + 344 p.
JORDAN, C. Calculus of Finite Differences. Budapest, Eggenberger Book Shop, 1939, xxi + 654 p.
KOWALEWSKI, G. Interpolation und genaherte Quadratur. Leipzig, Teubner, 1932, vi + 146 p.
LACR0IX, S. F. Traite du Calcul Differentiel et du Calcul Integral. Troisieme Partie. Des Differ-
ences et des Series. Paris, Courcier, 2nd ed. 1819, xxiv + 776 p.
LACR0IX S. F. Trait/ Elementaire de Calcul Differentiel et de Calcul Integral, vol. 2. Paris, Mallet-
Bachelier, 6th ed. 1862, viii + 491 p., p. 1-104.
DE LAGNY,T. F. Methodes nouvelles pour former et resoudre toutes les equations. Hist.Acad.Sci. Paris
1705, 277-300 (1705).
DE LAGNY,T. F. Traite des progressions arithmetiques de tous les degres. Hist. Acad. Sci. Paris
1722, 264-320 (1722).
LAGRANGE, J. L. Sur une nouvelle espece de calcul relatif a la differentiation et a 1« integration.
Oeuvres de Lagrange, vol. 3. Paris, Gauthier-Villars, 1869, p. 439-476.
361
BIBLIOGRAPHY
LAPLACE, P. S. Theorie analytique des probabilites, 3rd ed., book 1. Oeuvres completes de Laplace,
vol. 7. Paris, Gauthier-Villars, 1886, p. 7-180.
LAPLACE, P. S. Memoire sur la usage du calcul aux differences partielles dans la theorie des suites.
Oeuvres, vol. 9, 1893, p. 311-335. See also Memoire sur les suites. Oeuvres, vol. 10, 1894,
p. 1-89.
LAURENT, H. Traite^ d» Analyse, vol. 1. Paris, Gauthier-Villars, 1885, xL + 392 p., p. 97-118.
LEGENDRE, A. M. Exercices de calcul integral, vol. 2. Paris, Courcier, 1817, xx+ 544 p., p.72-96,
131-136.
LEGENDRE, A. M. Traite des fonctions elliptiques et des integrales Euleriennes. Vol„2.Paris, Huzard
Courcier, 1826, viii + 596 p., p. 1-120.
LEHMER, D. H. On the maxima and minima of Bernoulli polynomials. Amer. Math. Month. 47, 533-538
(1940).
LIDSTONE, G. J. Notes on interpolation. Jour. Inst. Actuar. 71, 68-95 (1941).
LOWAN, A. N. On the computation of the second differences of the Si(x), Ei(x) and Ci(x) functions.
Bull. Amer. Math. Soc. 45, 583-588 (1939).
MARKOFF, A. A. Differenzenrechnung. Leipzig, Teubner, 1896, v + 194 p.
MKELADZE, S. Ober dividierte Differenzen mit wiederholten Argumentwerten. Trav. Inst. Math.
Tbilissi (Trudy Tbiliss. Mat. Inst.) 9, 49-60 (1941).
DE MOIVRE, A. De fractionibus algebraicis radicalitate immunibis ad fractiones simplicores reducendis
deque summandis terminis quarumdam serierum aequallo intervallo a se distantibus. Phil.
Trans. Roy. Soc. Lond. 32, 162-178 (1722-1723).
DE MOIVRE, A. Miscellanea analytica de seriebus ed quadratis. London, Tonson and Watts, 1730.
DE MONTHORT, P. R. De seriebus infinitis tractatus. Phil. Trans. Roy. Soc. Lond. 30, 633-675 (1717-
1719) .
M00T0N, G. Observationes diametrorum Solis et Lunae... Book III, chap. 3: De nonnullis numerorum
proprietabus. Lyon, Liberal, 1670, p. 268-395.
NEWTON, I. Methodus differentialis. In vol. 1 of Isaaci Newtoni Opera... Samuel Horsley,ed.London,
J. Nichols, 1779, p. 521-528.
NICOLE, F. Traite du calcul des differences finies. Hist. Acad. Sci. Paris: 1717, 7-21: 1723. 20-
37, 181-198; 1724, 138-158.
n „
NORLUND, N. E. Vorlesungen uber Differenzenrechnung. Berlin, Springer, 1924, ix + 551 p.
NORLUND, N. E. Sur la "Sorame" d'une fonction. Mem. des Sci Math., Fasc. 24, Paris, Gauthier-
Villars, 1927, 54 p.
PASCAL, E. Calcolo delle variazioni e calcolo delle differenze finite. Part 3 of Lezioni de calcolo
infinitesimale. Milan, Hoepli, 1897, xii + 330 p., p. 207-330.
PERL, E. Untersuchungen liber Differenzenkoefficienten erster und zweiter Art...(Koenigsberg Diss.).
Leipzig, Hoffman, 1911, 126 p.
PINCHERLE, S. and AMALDI, U. Le operazioni distributive e le loro applicazioni all' analisi. Bologna,
Zanichelli, 1901, xii + 490 p.
DE PRONY, G. C. Cours d'analyse appliquee a La mecanique. Jour. Ecole Polytech. Paris: 1 (1). 107-
119; 1 (2), 1-23; 1 (3), 209-273; 1 (4), 459-569 (1796-1797).
RICHARDSON, L. F. The deffered approach to the limit I. Single lattice. Phil. Trans. Roy. Soc. Lond.
A226, 299-349 (1927).
362
BIBLIOGRAPHY
RUSSELL. W. H, L, On the calculus of finite differences. Mesa, of Math. (2) 11, 33-36 (1881-1882).
SALZER, H. E. Table of coefficients for differences in terms of derivatives. Jour. Math. Fhys.
(M.I.T.) 23, 210-212 (1944).
SCHLOMILCH, 0. Theorie der Differenzen und Suramen. Halle, Schmidt, 1848, v + 241 p.
SCHWEINS, F. Theorie der Differenzen und Differentials . Heidelberg, 1825, vi + 666 p., p. 1-113*
SELIWANOFF, D. Lehrbuch der Differenzenrechnung. Vol. 13 of Teubners Sammlung von Lehrbuchern.
Leipzig, Teubner, 1904, vi + 92 p.
STEFFENSEN, J. F. Note on divided differences. Danske Vid. Selsk. Math.-Fys. Medd., 17,No. 3, 12 p.,
1939.
STIRLING, J. Methodus differentialis Newtoniana illustrata. Phil. Trans. Roy. Soc. Lond.30, 1050-
1070 (1717-1719).
STIRLING, J. Methodus differentialis: sive Tractatus de summatione et interpolatione serierum
infinitarum. London, Whiston and White, 1754, iv + 154 p.
STURM, C. Cours d'Analyse, vol. 2. Paris, Mallet-Bachelier, 1859, P» 231-257.
TAYLOR, B. Methodus incrementorum directa ed inversa. London, Innys, 1717, vi + 119 p.
TAYLOR, B. De seriebus infinitis tractatus. Appendix, qua methodo diversa eadem materia tractatur.
Phil. Trans. Roy. Soc. Lond. 30, 676-689 (1717-1719).
TIMERDING, H. E. Differenzenrechnung. Chap. 9, vol . 1 (1) of Pascal's Repertorium der hoheren Ana-
lyse, Leipzig, Teubner, 2nd ed- 1910*
LE TERRIER, U. J. Recherches astronomiques. Ann. de l'Observ. Paris, 1, 122-128, 151-154 (1855).
14. DIFFERENCE EQUATIONS
BIRKH0FF, G. D. Note on linear difference and differential equations. Proc. Nat. Acad. Sci. U.S.A.
27,65-67 (1941).
BLEICH, F. and MELAN, E. Die gewohnlichen und partiellen Differensengleiehungsn der Baustatik.
Berlin, Springer, 1927, vii +■ 350 p.
BSffiffiR, P. E. Differenzengleichungen und Bestimmte Integrale. Leipzig, Koehler, 1939, vi +■ 148 p.
CHARLES, J. A. C. Integral (Calcul integral des equations en differences finies). Ency. Meth.,
Math. Vol. 2, p. 221-225. Paris, 1789.
C0URN0T, M. Traite elementaire de la theorie des fonctions et du calcul infinitesimal, vol.2.Paris,
Hachette, 2nd ed. 1857, 533 p., p. 431-480.
FUNK, P. Die linearen Differenzengleichungen und ihre Anwendung in der Theorie der Baukonstruktionen.
Berlin, Springer, 1920, 84 p.
GERONIMUS, J. Sur quelques equations aux differences finies et les syst ernes correspondents des
polynomes orthogonaux. C. R. (Doklady) Acad. Sci. URSS (N.S.) 29, 536-538 (1940).
HEYMANN, W. Studien iiber die Transformation und Integration der Differential- und Differenzen-
gleichungen. Leipzig, Teubner, 1891, x +■ 436 p.
ISAACS, R. P. A finite difference function theory. Univ. Nac. Tucuman. Revista A. 2, 177-201 (1941).
363
BIBLIOGRAPHY
JORDAN, C. Calculus of Finite Differences. Budapest, 1939. (See sect, 13, Jordan, C).
LANCASTER, 0. E. Sequences defined by non-linear algebraic difference equations. Ann. of Math. (2)
42, 251-280 (1941).
LAURENT, P. M. Traite d»analyse. Paris, Gauthier-Villars, 1890, vol. 6. (Calcul integral. Equations
differentielles partielles, iv + 339 p.).
N0RL0ND, N. E. Vorlesungen uber Differenzenrechnung. Berlin, Springer, 1924, ix + 551 p.
OLTRAMARE, G. Calcul de generalisation. Paris, Hermann, 1899, viii + 191 p.
PASCAL, E. Repertorium der hoheren Mathematik. Art. by Guldberg, vol. I 2 , p. 555-560.
RACLIS, R. Solution principals de 1* equation lineaire aux differences finies. Acta Math. 55, 277-
394 (1930).
SPOERL, C. A. A fundamental proposition in the solution of simultaneous linear equations. Trans.
Actuar. Soc. Amer. 44, 276-288 (1943).
SPOERL, C. A. Difference-equation interpolation. Trans. Actuar. Soc. Amer. 44, 289-325 (1943).
WEINNOLDT, E. H. F. Uber Funktionen welche gewisse Differenzengleichungen n. Ordnung Genuge leisten
(Diss., Kiel). Kiel, Lipsius and Tischer, 1885, 41 p.
15. DIRECT INTERPOLATION
A. Functions of a Single Variable
ABASON, E. Sur l 1 approximation minimum d'ordre n sur un ensemble de n + 2 points. Bull. Sci. Ec.
Polyt. Timifoara 3, 64-67 (1930).
ABASON, E. Sur la condition pour que n +■ 2 points soient situes sur une parabole du n-ieme degre.
Bull. Soc. Sci. Cluj 5, 188-190 (1931).
AITKEN, A. C. On a generalisation of formulae for polynomial interpolation. Jour. Inst. Actuar.
61, 107-112 (1930).
AITKEN, A. C. On interpolation by iteration of proportional parts, without the use of differences.
Proc. Edin. Math. Soc. (2) 3, 56-76 (1932).
AMPERE, A. M. Essai sur un nouveau mode d* exposition des principes du calcul differentiel, du calcul
aux differences et de 1' interpolation des suites considerees comme derivant d'une source
commune. Ann. Math. (Gergonne) 16, 329-349 (1825-26).
AND0YER, H. Calcul des differences et interpolation. Vol. I, part 21 in 1 (4), Fasc. 1 of Ency. des
Sci. Math., 1906, p. 47-160.
ARBOGAST, L. F. A. Du calcul des derivations. Strasbourg, Levrault, 1800, xxii + 404 p., p. 375-404.
BAUSCHINGER, J. Interpolation. Part I D 3 of Ency. der Math. Wiss., 1(2). Leipzig, Teubner, 1901,
p. 799-820.
BAUSCHINGER, J. Tafeln zur theoretischen Astronomie. Leipzig, Engelmann, 1901, iv + 148 p.
BEIARDINELLI, G. II problema dell'interpolazione. Rend. Sem. Mat. Fis. MiLano 3, 13-28 (1930).
BENNETT, A. A. The interpolations! polynomial. Chap. 1 of Numerical Integration of Differential
Equations. (Report of Committee on Numerical Integration). Bull. Nat. Res. Council, No. 92,
p. 11-50 (1933).
364
BIBLIOGRAPHY
BIERMANN,0. Vorlesungen uber mathematische Naherungsmethoden. Braunschweig, Vieweg, 1905, ix + 227p.,
p. 92-169.
BLANCH, G. and RHODES, I. Seven-point Lagrangian integration formulas. Jour. Math. Phys. (M.I.T.)
22, 204-207 (1943).
BOOLE, G. A Treatise on the Calculus of Finite Differences. London, Macmillan, I860, iv + 248 p.
BOYER, J. Oscillatory interpolation in practice. Record Amer. Inst. Actuar.: 31* 337-350(1942^; 32,
83-96 (1943).
BRAUNSCHMIDT, 0. Uber Interpolation. Jour. Reine Angew. Math. 185, 14-55 (1943).
CAJORI, F. A History of Mathematical Notations, Vol. 2. Chicago, Open Court, 1929, xviii + 367 p.,
p. 42-43, 263-267.
CAMP, K. Actuarial notes practical interpolation methods with second-order curves. Trans. Actuar.
c a_ s — i.n i.*>£_j.«ao ftty3o\
CAUCHY, A, L. Cours d'analyse de l'ecole royale polytechnique. I partie, analyse algebrique. Note V.
Sur la formule de Lagrange relative a 1' interpolation. Oeuvres completes d'Augustin Cauchy,
2nd series, vol. 3, Paris, Gauthier-Villars, 1897, F* 429=433*
CADCHY, A. L. Sur les fonctions interpolaires. Oeuvres completes d'Augustin Cauchy, 1st series,
vol. 5. Paris, Gauthier-Villars, 1885, p. 409-424.
CHARLES, J. A. C. Interpolation (mathematiques et physique). Ency. Meth.,Math. Vol. 2, p. 233-237,
Paris, 1789.
CLAUSEN, T. Uber mechanische Quadra turen. Jour. Reine Angew. Math. 6, 287-289 (1830).
C0MRIE, L. J. Interpolation and Allied Tables. Reprint from the Nautical Almanac for 1937. London,
H. M. Stationery Office, 1936, 45 p.
CR0UT, P. D. A method for deriving formulas of interpolation. Jour. Math. Phys. (M.I.T. )8, 18-55,
119-128 (1929) :
DAVIS, H. T. Tables of the Higher Mathematical Functions, vol. 1. Bloomington, Indiana, Principia
Press, 1933, xiii+ 377 p., p. 65-100.
DeMORGAN, A. The Differential and Integral Calculus. London, Baldwin and Cradock, 1842, Chap. 18,
p. 542-560.
DIESTEL, F. Bsitrage su der Interpclaticnsrechnung. (Gcttingen Diss.), Gcttingen, Vandenhoeck and
Ruprecht, 1890, 47 p.
ECHOLS, W. H. On some forms of Lagrange's interpolation formula. Ann. of Math. (1) 8, 22-24 (1893).
EGGER, H. Praktische Interpolation. Zeit. Angew. Math. Mech. 22, 362-364 (1942).
ENCKE, J. F. uber Interpolation. Gesammelte mathematische und astronomische Abhandlungen von J. F.
Eneke, vol. 1. Berlin, Dummler, 1888, p. 1-20.
ERDOS, P. and TURAN, P. On interpolation. Ann. of Math. (2): 38, 142-155 (1937) ;39, 703-724 (1938);
41, 510-533 (1940).
EVERETT, J. D. On the algebra of difference tables. Quart. Jour. Pure Appl. Math. 31,357-376 (1900).
EVERETT, J. D, On interpolation formulae. Quart. Jour. Pure Appl. Math. 32, 306-313 (1901).
FAVARD, J. Sur i ! interpolation. Bull. Soc. Math. France 67, 102-113 (1939).
FAVARD, J. Sur 1' interpolation. Jour. Math. Pures Appl. (9) 19, 281-306 (1940).
365
BIBLIOGRAPHY
FEJER, L. Uber Interpolation. Naehr. Ges. Wiss. Gottingen p. 66-91 (1916).
FEJER, L. Uber Interpolation und konforme Abbildung. Nachr. Ges. Wiss. Gottingen p. 319-331 (1918).
FEJER, L. Uber Weierstrasssche Approximation, besonders durch Hermitesche Interpolation. Math. Ann.
102, 707-725 (1929).
FEJER, L. Lagrangesche Interpolation und die zugehorigen konjugierten Punkte. Hath. Ann. 106, 1-
55 (1932).
FEKETE, M. Uber Interpolation. Zeit. Angew. Math. Mech. 6, 410-413 (1926).
FELLER, W. On A. C. Aitken's method of interpolation. Quart. Appl. Math. 1, 86-87 (1943).
FISHER, R. A. and W3SHART, J. On the distribution of error of an interpolated value and on the con-
struction of tables. Proc. Camb. Phil. Soc. 23, 912-921 (1927).
FORSYTH, C. H. An Introduction to the Mathematical Analysis of Statistics. New York, Wiley, 1924.
Chap. 3, p. 33-55.
FRASER, D. C. Newton's interpolation formulas. Jour. Inst. Actuar.:51, 77-106, 211-232 (1919); 52,
117-135 (1921).
FRASER, D. C. Newton's Interpolation Formulas. London, Layton, 1927, iv + 95 p.
GIBB, D. A Course in Interpolation and Numerical Integration. Edin. Math. Tracts. No. 2. London,
Bell, 1915, viii + 90 p.
GLOVER, J. W. Interpolation, summation and graduation. Chap. 3 of Handbook of Mathematical Sta-
tistics. Boston, Houghton-Mifflin, 1924, p. 34-61.
GONTCHAROFF, M. Sur quelques series d* interpolation generalisant celles de Newton et de Stirling.
(Russian. French summary.). Uchenye Zapiski Moskov. Gos. Univ. Mat. 30, 17-48 (1939).
GREVILLE, T. N. E. A generalization of Waring's formula. Ann. Math. Statist. 15, 218-219 (1944).
GRUNWALD, G. On a convergence theorem for the Lagrange interpolation polynomials. Bull. Amer. Math.
Soc. 47, 271-575 (19U).
GRUNWALD, G. Note on interpolation. Bull. Amer. Math. Soc. 47, 257-260 (1941).
HADAMARD, J. Cours d'analyse, vol. I. Paris, Hermann, 1925, p. 132-151.
HEINHOLD, J. Zur Interpolation bei ungleichen Tafelabstanden. Zeit. Angew. Math. Mech. 22, 235-238
(1942).
HENDERSON, R. and SHEPPARD, H. N. Graduation of Mortality and Other Tables. Actuarial Studies No.
4. New York, Actuarial Soc. of Amer., 1919, v +■ 82 p.
HEHMTTE, C. Sur la formule d' interpolation de Lagrange. Jour. Rein* Angew. Math. 84, 70-79 (1878).
ISSERLIS, L. Note on Chebysheff's interpolation formula. Biometrika 19, 87-93 (1927).
JACKSON, D. The Theory of Approximation. Amer. Math. Soc. Colloquium Pubis., vol. 11. New York,
Amer. Math. Soc, 1930, viii + 178 p.
JACKSON, D. Fourier Series and Orthogonal Polynomials. Carus Monograph Series, No. 6. Oberlin, Ohio,
Math. Assoc. Amer., 1941, xii + 234 p.
JOFFE, S. A. Interpolation formulae and central-difference notation. Trans. Actuar. Soc. Amer. 18,
72-98 (1917).
JORDAN, C. Cours d'analyse de l'ecole polytechnique, vol. 2. Paris, Gauthier-Villars, 3rd ed. 1913,
705 p., p. 125-132.
366
BIBLIOGRAPHY
JORDAN, G s Statistique E>athe»atique, Paris, Gauthier-Villars, 1927, xvii + 344 P.
EAMKNhTZKT X* M. Sur 1' interpolation au moyen des deri^ees et les procedes d' interpolation corres—
pondants. I, II. C. R. (Doklady) Acad. Sci. ORSS (N.S.):25, 356-358 (1939); 26, 217-219
(1940).
KING, G. Institute of Actuaries' Text Book of the Principles of Interest, Life Annuities, and As-
surances, and their Practical Application. Part II. Life Contingencies. London, Layton, 2nd
ed. 1902, xxxi + 569 p., p. 420-457.
KOWALEWBKI, A rf Newton, Cotes, Gauss, Jacobi. Vier grundlegende Abhandlungen uber Interpolation und
genahrte Quadratur. Leipzig, Veit, 1917, vi -h 104 P.
KOWALEWSKI, G. Interpolation und genaherte Quadratur. Leipzig, Teubner, 1932, v + 146 p.
LAGRANGE, J. L. Sur une methode particuliere d« approximation et interpolation. Oeuvres de Lagrange,
vol. 5. Paris, Gauthier-Villars, 1870, p. 517-531.
LAGRANGE, J. L. Sur les interpolations. Oeuvres, vol. 7, 1877, p. 533-553.
LAGRANGE, J. L. Memoire sur la methode d» interpolation. Oeuvres, vol. 5, 1870, p. 661-684.
LAURENT, P. M. H. Traite d'analyse, vol. 3. Paris, Gauthier-Villars, 1888, 511 p., p. 418-497.
LEVER, E. H. On obtaining the values of life annuities at isolated rates of interest. Jour. Inst.
Actuar. 52, 171-179 (1921).
LIDSTONE, G. J. Notes on Everett's interpolation formula. Proc. Edin. Math. Soc. 40, 21-26 (1921-
1922).
LIDSTONE, G. J. Notes on interpolation. Jour. Inst. Actuar. 71, 68-95 (1941).
LINDOW, M. Numerische Infinitesimalrechnung. Berlin, Dummler, 1928, viii + 176 p.
DE LOSADA I PUGA, C. The interpolation formula of Stirling deduced from Taylor's series. (Spanish).
LOSDEKY, S. Sur le procede d' interpolation de Fejer. C. R. (Doklady) Acad. Sci. URSS (N,S.) 24,
318-321 (1939).
LOWAN, A. N. and SALZER, H. E. Formulas for complex interpolation. Quart. Appl. Math. 2, 272-274
(1944).
MAENNCHEN, P. uber ein Interpoiationsverfahren des jugendlichen Gauss. Jber. Deutsch Math. Verein
28, 80-84 (1919).
MARKOFF, A. A. Differenzenrechnung. Leipzig, Teubner, 1896, v + 194 p.
MAZZONI, P. Su un metodo d'interpolazione. Boll. Un. Mat. Ital. 8, 29-39 (1929).
MAZZONI, P. Alcune applicazioni dei polinond di Tchebychev. Boll. Un. Mat. Ital. 8, 246-248 (1929).
MAZZONI, P. Sul metodo d'interpolazione di Tchebychev. Boll. Un. Mat. Ital. 9, 132-141 (1930).
McCLINTQCK, E. A new general method of interpolation. Amer. Jour. Math. 2, 307-314 (1879).
MIRAKTAN, G. \-* m Approximation des f onctions continues au moyen de polynoraes de la forme
e -nx }_> jkc c . R# (Doklady) Acad. Sci. URSS (N.S.) 31, 201-205 (1941).
MONTEL, P. Lecons sur les series de polynomes a. une variable conplexe. Coll. Borel, Paris, Gauthier-
Villars, 1910.
NEWTON, I. Methodus differentialis. In vol. 1 of Isaaci Newtoni opera quae exstant omnia, Samuel
Horsley, ed. London, 1779, p. 521-528.
367
BIBLIOGRAPHY
NIELSEN, N. Traite elementaire des nombres de Bernoulli. Paris, Gauthier-Villars, 1923, x + 398 p.
n n
NORLUND, N. E. Vorlesungen uber Differenzenrechnung. Berlin, Springer, 1924, ix + 551 p.
ii
NORLUND, N. E. Lemons sur les series d» interpolation. Coll. Borel, Paris. Gauthier-Villars. 1926.
vii+ 236 p. '
OGURA, K. Sur la theorie de 1' interpolation. C. R. Congr. Intern. Math. Strasbourg, 1920, p. 316-
322, Toulouse, Edouard Privat, 1921.
PEANO, G. Residuo in formula de quadratura Cavalieri-Simpson. L'Ens. Math. 18, 124-129 (1916).
PEARSON, K. Tracts for Computers, No. 2. On the Construction of Tables and on Interpolation. Part
I, Uni-variate Tables. Cambridge, Cambridge Univ. Press, 1920, 70 p.
PIPES, L. A. The method of symmetrical components applied to harmonic analysis. Phil. Mag. (7) 29,
66-74 (1940).
QUADE, W. Abschatzungen zur trigonometrischen Interpolation. Deutsche Math. 5, 482-512 (1941).
RADAU, R. Etudes sur les formules d' interpolation. Paris, Gauthier-Villars, 1891, 96 p.
RICE, H. L. The Theory and Practice of Interpolation. Lynn (Mass.), Nichols, 1899, 234 p.
RUTLEDGE, G. The explicit determination of Cotes' coefficients for polynomial area. Jour. Math.
Phys. (M.I.T.) 1, 78-85 (1922).
RUTLEDGE, G. The polynomial determined by 2n + 1 points. Jour. Math. Phys. (M.I.T.) 2,47-62(1923).
RUTLEDGE, G. Limiting values of Lagrangean coefficients. Jour. Math. Phys. (M.I.T.) 8, 13-17 (1929).
SAMUELSON, P. A. A simple method of interpolation. Proc. Nat. Acad. Sci. U.S.A. 29, 397-401 (1943).
SHEPPARD, W. F. Interpolation. Encyclopaedia Britannica 11th ed., 14, 706-710 (1910).
SHEPPARD, W. F. Mathematics for the study of frequency statistics. Math. Gaz. 15, 232-249 (1930).
SHOHAT, J. Application of orthogonal Tchebycheff polynomials to Lagrangean interpolation and to the
general theory of polynomials. Ann. Mat. Pura Appl. 18, 201-238 (1939).
SPOERL, C. A. Difference-equation interpolation. Trans. Actuar. Soc. Amer.: 44, 289-325 (1943);
45> 70-82 (1944).
STEFFENSEN, J. F. Interpolation. Baltimore, Williams and Wilkins, 1927.
STOCK, J. S. A method of graphic interpolation. Jour. Amer. Statist. Assoc. 34, 709-713 (193?) .
TAYLOR, B. Methodua incrementorum directa et inversa. London, Innys, 1717, 118 p.
THIELE, T. N. Interpolationsrechnung. Leipzig, Teubner, 1909, xii + 175 p.
VERNOTTE, P. Sur la representation d'une fonction experimentale par une fraction rationnelle. C. R-
Acad. Sci. Paris 213, 433-435 (1941). •"»•»<. *•
WEBSTER, M «J • *°*« on certain Lagrange interpolation polynomials. Bull. Amer. Math. Soc. 45, 870-
°73 ^1939/.
IHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 3rd ed. 1942.
chaps. 1, 2 and 3, also p. 369-371.
WILLERS, F. A. Benutzung projektiver Stolen zur Unterteilung von Skalen anderer Funktionen. Zeit.
Angew. Math. Mech. 20, 291-292 (1940). ^^^
368
BIBLIOGRAPHY
B« Functions of Several Variables
BIERMAHN, 0. fiber naherungsweise Cubaturen. Monatsh. Math. Phys. 14, 211-225 (1903).
BROWN, E. H. and BORN, J. Elements of Finite Differences. London, Layton,1915, 289 P., P. 45-61.
ELDERTON, W. P. Some notes on interpolation in n-dimension space. Biometrika 6, 94-103 (1908).
KRONECKER, L. Dber einige Interpolationsformeln fur ganze Functionen mehrerer Variablen (1869). Ges.
Werke, Vol. I. Leipzig, Teubner, 1895, p. 135-141.
LAGRANGE, J. L. Sur une nouvelle espece de calcul relatif a la differentiation et a l'integration
des quantites variables. Oeuvres de Lagrange, vol. 3. Paris, Gauthier-Villars, 1869, p. 441-
476.
LAL, D. N. and DASGUPTA, P. N. Interpolation polynomials in two and more variables. Bull. Calcutta
Math. Soc. 32, 7-14 (1940).
LAMBERT J. H. Beytrage zum Gebrauche der Mathematik und deren Anwendung. Theil III. Anmerkungen
* uber das Einschalten. Berlin, Buchandlung der Realschule, 1772, p. 66-104.
vismrr « <;»,«» fn^ts-An -.n t-h« thsorv of interDelation of many independent variables. T8hoku Math.
Jour. 18, 309-321 (1920).
PEARSON, E. On the Construction of Tables and on Interpolation. Part II. Bi-variate Tables. Tracts
for Computers, No. III. Cambridge, Cambridge Univ. Press, 1920, 54 p.
ROURE H. Sur une generalisation de la serie de Lagrange, avec applications a l»astronomie. C. R.
' Acad. Sci. Paris 216, 332-353 (1943).
IffllTTAKER, E.T. and R0BINS0N,G. The Calculus of Observations. London,Blackie, 3rd ed.1942, p.371-374.
16. INVERSE INTERPOLATION, TABULATION AND SUBTABULATION
AITKEN, A. C. On interpolation by iteration of proportional parts, without the use of differences.
Proc. Edin. Math. Soc. (2) 3, 56-76 (1932).
COMRIE, L. J. On the construction of tables by interpolation. Month. Not. Roy. Astr. Soc. 88, 506-
523 (1928).
COMRIl, L. J. Inverse interpolation. Nautical JOaanac, 1937. London, H. M. Stationery Office, 1936 5
p. 934-939.
PEANO, G. Interpolazione nelle tavole numeriche. Atti Accad. Sci. Torino 53, 693-716 (1917).
PEARSON, K. Tracts for Computers, No. II. On the Construction of Tables and on Interpolation. Part
I- Uni-variate Tables. London, Cambridge Univ. Press, 1920, 70 p.
SALZER H. E. A new formula for inverse interpolation. Bull. Amer. Math. Soc. 50, 513-516 (1944).
VAN ORSTRAND, C. E. Inverse interpolation by means of a reversed series. Phil. Mag. (6) 15, 628-638
(1908).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. London, Blackie, 3rd ed. 1942, p.
53-57, 60-61, 96-98.
1? s INTERPOLATION TABLES
nnMFIE- L- J- Tables for interpolation to tenths and fifths by the end-figure process. Nautical Alma-
' "nac, 1931. London, H. M. Stationery Office, 1929, p. 828-859.
369
BIBLIOGRAPHY
COMRIE, L. J. Interpolation and Allied Tables. Reprint from Nautical Almanac for 1937, London, H. M.
Stationery Office, 1936, 45 p.
COMRIE, L. J. and HARTLEY, H. 0. Table of Lagrangian coefficients for harmonic interpolation in
certain tables of percentage points. Biometrika 32, 183-186 (1941).
DAVIS, H. T. Tables of the Higher Mathematical Functions, vol. 1. Bloomington, Indiana, Principia
Press, 1933, xiii + 377 p., p. 101-176.
GLOVER, J. W. Tables of Applied Mathematics in Finance, Insurance, Statistics. Ann Arbor, George
Wahr, 1930, xiii + 678 p., p. 414-433.
HENDERSON, R. and SHEPPARD, H. N. Graduation of Mortality and Other Tables. Actuarial Studies No.
4. New York, Actuar. Soc. of Amer., 1919, vi + 82 p.
HUNTINGTON, E. V. Tables of Lagrangean coefficients for interpolating without differences. Proc.
Amer. Acad. Arts Sci. 63, 421-437 (1929).
LAMPE, E. Zur mechanischen Quadratur. Jber. Deutsch. Math. Verein 25, 325-332 (1917).
LITTLE, A. S. A Table of Interpolation Multipliers. London, Rutledge, 1927.
LOWAN, A. N. and SALZER, H. E. Coefficients for interpolation within a square grid in the complex
plane. Jour. Math. Phys. (M.I.T.) 23, 156-166 (1944).
MATH. TABLES PROJECT (W.P.A.). Tables of Lagrangian Interpolation Coefficients. New York, Columbia
Univ. Press, 1944, xxxvi + 392 p.
RUTLEDGE, G. Explicit determination of Cotes' coefficients for polynomial area. Jour. Math. Phys.
(M.I.T.) 1, 78-85 (1922).
RUTLEDGE, G. The polynomial determined by 2n + 1 points. Jour. Math. Phys. (M.I.T.) 2, 47-62 (1922).
RUTLEDGE, G. Fundamental table for Lagrangean coefficients. Jour. Math. Phys. (M.I.T.) 8, 1-12(1929).
RUTLEDGE, G. and CROUT, P. D. Tables and methods of extending tables for interpolation without
differences. Mass. Inst, of Tech. Pubis. (Dept. of Math.) Ser. 2, No. 176, July, 1930, p.
166-180.
SALZER, H. E. Table of coefficients for inverse interpolation with central differences. Jour. Math.
Phys. (M.I.T.) 22, 210-224 (1943).
SALZER, H. E. Table of coefficients for inverse interpolation with advancing differences. Jour.
Math. Phys. (M.I.T.) 23, 75-102 (1944).
THOMPSON, A. J. Table of Coefficients of Everett's Central-Difference Interpolation Formula. Tracts
for Computers, No. 5. Cambridge, Cambridge Univ. Press, 2nd ed. 1943, viii + 32 p.
18. ASYMPTOTIC EXPANSIONS
BARNES, E. W. The asymptotic expansion of integral functions defined by Taylor's series .Phil.Trans.
Roy. Soc. Lond. 206A, 249-297 (1906).
BARNES, E. W. The asymptotic expansion of integral functions defined by generalised hypergeometric
series. Proc. Lond. Math. Soc. (2) 5, 59-116 (1907).
BARNES, E. ff. A new development of the theory of the hypergeometric functions. Proc. Lond. Math.
Soc. (2) 6, 141-177 (1908).
370
BIBIIOGRAPHI
BOLZA, 0. Gsber die linearen Relatione* zwischen den zu verschiedenen sin|ul£ren Punkten gf^gen
' Fundamentalsystemen yon Integralen der Riemann' schen Differentialgleichung. Math. Ann. **,
526-536 (1893).
BOHEL, E. Lemons sor les series divergentes. Coll. de Monographies sur la Th^orie des Fonctions.
Paris, Gauthier-Villars, 2nd ed. 1928, 260 p.
FORD W. B. Studies on Divergent Series and Susmability. Mich. Sci. Series vol. II. New York,
' * Macmillan, 1916, xi + 194 P.
FORD, W. B. On the behavior of integral functions in distant portions of the plane. Bull. Amer.
Math. Soc. 34, 91-106 (1928).
FORD W. B. The Asymptotic Developments of Functions defined by Maclaurin Series. Univ. of Mich.
FORD, W. B - tudies 1 > n ^ ci ^ fic Series v S7 n . Ann Arbor, Univ . of Mich. Press, 1936, viii + 143 p.
HAAR, A. Uber asymptotische Entwicklungen von Funktionen. Math. Ann. 96, 69-107 (1927).
JACOBSTHAL, W. Asymptotische Darstellungen von Losungen linearer Differentialgleichungen. Math. Ann.
56, 129-154 (1902).
,~« « ^ ,__*..*_ ****** a «i,rM«n« «? Unmr differential equations of the second order,
J ™"°' S; certain*^^^ On the "modified Mathieu's equation.
Proc. Lond. Math. Soc. 23, 428-454 (1924).
KNOPP K. Theory and Application of Infinite Series. (Translation of 2nd German ed., by R.C. Young.).
' London, Blackie, 1928, xii + 571 p., p. 520-563.
t iisr-TO s tt The a svMDt otic solutions of ordinary linear differential equations of the second
LAHGER, R.^ ^ ^ecialTeference to the Stokes phenomenon. Bull. Amer. Math. Soc. 40, 545-582
(1934).
LENSE, J. Reihenentwicklungen in der mathematischen Physik. Berlin, de Gruyter, 1933, 178 p., p. 145-
162.
-...__ _--_*__ jj *.-.«, -+ t«= r n ™+A nr >a H«fMrvlfts nar un develoDT>ement de Taylor. Ann.
Toulouse 2, 317-430 (1900).
LITTLEW00D J. E. On the asymptotic approximation to integral functions of zero order. Proc. Lond.
Math. Soc. (2) 5, 361-410 (1907).
P0INCAHB, H. Lea methodes nouvelles de la mecanique celeste, vol. 2. Paris, Gauthier-Villars, 1893,
' viii + 479 p.
PUGACH0V, V. S. Evaluation of error of asymptotic representations of integrals of linear differ-
ential equations containing a parameter. (Russian. English summary.!. Appl. Math. Mech.
(Akad. Nauk SSSR. Prikl. Mat. Mech.) 6, 203-208 (1942).
..-re™, r. w. i Tr^tise on the Theory of Bessel Functions. Cambridge and New York, Cambridge Univ.
"" ' ~"press (Macmillan), 2nd ed. 1944, vi + 804 p., p. 194-270.
WHITTAKER, E. T. and WATSON, G. N. Modern Analysis. Cambridge, Cambridge Univ. Press, 1944, 608 p.,
'chap. VIII, p. 150-159.
wtottntckr W Einiee Arwendungen der Euler-Maclaurinsche Summenformel, insbesondere auf eine
Aufgabe von Abel! Acta Math. 26, 255-271 (1902).
WRIGHT E. M. The asymptotic expansion of the generalized hypergeometric function. Proc. Lond. Math.
' Soc. (2) 46, 389-408 (1940).
WRIGHT E M. The asymptotic expansion of integral functions defined by Taylor* s series. Phil.
* *Trans. Roy. Soc. Lond. 238A, 423-451 (1940).
371
BIBLIOGRAPHY
19. NUUERICAL DIFFERENTATION AND HIGHER DERIVATIVES
BABINI, J. On the application of finite differences to the successive derivation of composite func-
tions. (Spanish). Revista Union Mat. Argentina 8, 160-164 (1942),
BICKLET, W. G. Formulae for numerical differentiation. Math. Gaz. 25, 19-27 (1941).
BICKLEI, W. G. and MILLER, J. C. P. Numerical differentiation near the limits of a difference table.
Phil. Mag. (7) 33, 1-14 (1942).
BRUNS, H. Grundlinien des wissenschaftlichen Rechnens. Leipzig, Teubner, 1903, vii+159 p., p. 62-67.
CRANK, J., HARTREE, D. R., INGHAM, J. and SLOANE, R. W. Distribution of potential in cylindrical
thermionic valves. Proc. Phys. Soc. Lond. 51, 952-971 (1939).
GAUNT, A. The deferred approach to the limit. II. Interpenetrating lattices. Phil. Trans. Roy. Soc.
Lond. A226, 350-361 (1927).
HANSEN, P. A. Relationen einestheils zwischen Summen und Differenzen und anderntheils zwischen Inte-
gralen und Differentialen. Abh. Math. Phys. Klasse Konig. Sachs. Ges. Wiss. Leipzig 7, 507-
583 (I865) .
LINDOW, M. Numerische Infinitesimalrechnung. Berlin, Dumraler, 1928, viii + 176 p., chap. 2.
LOWAN, A., SALZER, H. E. and HILLMAN, A. A table of coefficients for numerical differentiation.
Bull. Amer. Math. Soc. 48, 920-924 (1942).
MARKOFF, A. A. Differenzenrechnung. Leipzig, Teubner, I896, vi + 194 p., p. 20-27.
VON OPPOLZER, T. Lehrbuch zur Bahnbestimmung der Kometen und Planeten. Vol. 2. Leipzig, Engelmann,
1880, p, 16-31.
SALZER, H. E. Coefficients for numerical differentiation with central differences. Jour. Math.
Phys. (M.I.T.) 22, 115-135 (1943).
SAUER, R. and P&SCH, H. Rechnerische Differentiation von Kurven. Zeit. Verein. Deutsch. Ing. 85
SCHWATT, I. J. An Introduction to the Operations with Series. Philadelphia, Univ. of Penn.Press
1924, vii + 287 p.
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 1942, p. 62-70.
20. NUMERICAL INTEGRATION OF DEFINITE INTEGRALS
A. Functions of a Single Variable
ABASON, E. Asupra unor formule pentru calculul cu aproximati al ariilor. Gaz. Mat. 36, 41-45 (1930).
ABAS0N,E. Sur la moyenne des fonctions paraboliques. Bull.Sci. Ec. Polyt. Timifoara 3, 235-243(1930).
ACHIESER, N. I. and KREIN, M. G. On some quadrature formulas of P. Tschebyscheff and A. Markoff
(Russian). Memorial volume dedicated to D. A. Grave. Moscow, 1940, p. 15-28.
AUBERT, P.^PAPELIER, G. Exercices de calcul numerique, vol. 2. Paris, Vuibert, 1920, 246 p.,
BACKMAN, G * krif M ^ od J k d | r theoretischen Wledergabe beobachteter Wachstumsserien. Lunds Univ. Ars-
372
BIBLIOGRAPHY
iwNBBPT, A- A, The interpolation polynomial. Chap. 1 of: Numerical Integration of Differential
~ ' Equations. (Report of Conndttee on Numerical Integration). Bull. Nat. Res. Councix, ho. y*,
Not. (1933), P. 11-50.
BERKELEY, E. C. Summation as a function of any terms. Record Amer. Inst. Actuar. 29, 314-348 U940).
BICKLEY, W. G. Formulae for numerical integration. Math. Gaz. 23, 352-359 (1939).
BERTRAND, J. Traite de calcul differentiel et decalcul integral. Vol. 2 Calcul faitfenl. Inte-
grales definies et indefinies. Paris, Gauthier-Villars, 1870, p. 331-352.
BIERMANN, 0. Zur naherungsweisen Quadratur und Cubatur. Monatsh. Math. Phys. 14, 226-242 (1903).
BOUNITZKY E. Remarque sur ia formule d»Euler-Maclaurin. Casopis pest. mat. a fys. (Prague) 57, 95-
*102 (1928).
BRUNS, H. Grundlinien des wissenschaftlichen Rechnens. Leipzig, Teubner, 1903, vii-H59 p., P- 68-
113.
CASSINA, U. Fonnole sommatorie e di quadratura ad ordinate estreme. Rend. 1st. Lombardo 72, 225-
274 (1939).
CASSINA, U. Formole sommatorie e di quadratura con l'ordinata media. Atti Accad.Sci. Torino 74,
300-325 (1939).
CASSINA, U. Estensione del teorema di Rolle al calcolo delle differenze ed application!. Rend. 1st.
Lombardo 72, 323-332 (1939).
CLAUSEN T. Uber mechanisehe Quadraturen. Jour. Reine Angew, Math. 6, 287-289 (1830).
CROUT P. D. A method for deriving formulas for the approximate calculation of integrals. Jour.
' Math. Phys, (M.I.T.)s 7, 126-159 (1928); 8, 119-128 (1929).
CROUT. P. D. An application of the invariant area properties of algebraic polynomials to the *«*-
CROUT, l^a of PP oraulas for mechanical integration. Jour. Math. Phys. (M.I.T.) 8, 200-215(1929).
CROUT P. D. The approximation of functions and integrals by a linear combination of functions.
' * Jour. Math. Phys. (M.I.T.) 9, 278-314 (1930).
CZUBER, E. Vorlesungen uber Differential- und Integralrechnung, vol. 2. Leipzig, Teubner, 3rd ed.
1913, P. 256-268.
DANIELL, P. J. Remainders in interpolation and quadrature formulae. Math. Gaz. 24, 238-244 (1940).
DUFTON, A. F. A new method for approximate evaluation of definite integrals between finite limits.
Nature 105, 355, 455-456 (1920).
ENCKE, J. F. Ueber mechanisehe Quadratur. Gesammeite mathematische und astronosaisehe Abhandlungsn
von J. F. Encke, vol. 1. Berlin, Dunnler, 1888, p. 21-60.
ENCKE, J. F. Ueber eine andere Methode, zu den Formeln der mechanischen Quadratur zu gelangen. Ges.
Abh., vol. 1, p. 61-99 (1888).
ENCKE, J. F. Ueber die Cotes'eschen Integrations-Factoren. Ges. Abh., vol. 1. p. 100-124 (1888).
FRANK P. and VON MISES, R. Die Differential-und Integralgleichungen der Mechanik und Physik. Vol. 1.
Braunschweig, Vieweg, 1930, p. 34-36, 289-292, 394-397, 467-469.
GAU, E. P. Calculs numeriques et graphiques. Collection Armand Colin, No. 60. Paris, Colin, 1925,
vi + 206 p., p. 107-120.
GERONIMUS, J. On Gauss 1 and Tchebychef f * s quadrature formulas. Bull. Amer. Math. Soc. 50, 217-221,
(1944).
373
BIBLIOGRAPHY
GIBB, D. A Course in Interpolation and Numerical Integration. Edin. Math. Tracts, No. 2.London, Bell.
1915, p. 63-90. ' *
GIRAUD, G. Sur une methode pour calculer les integrales. Bull. Sci. Math. (2) 48, 233-245 (1924).
GIRAUD, G. Sur le calcul numerique des integrales definies. Bull. Sci. Math. (2) 48, 397-412 (1924).
GROAT, B. F. Mean value of the ordinate of the locus of the rational integral algebraic function of
degree n expressed as a weighted mean of n+1 ordinates... Amer. Math. Month. 38, 212-219
GUERONIMUS, J. L. Sur l»erreur des quadratures mecaniques de Gauss. Bull. CI. Sci. PhyB. Math.
Kieff 4, 57-66 (1929).
GUERONIMUS, J. L. On some quadrature-formulae. Bull. Acad. Sci. URSS (Math. Phys.) (7) 3, 399-^08
HARROLD, O.^G. On the expansion of the remainder in the open-type Newton-Cotes quadrature formula.
Amer. Jour. Math. 59, 275-289 (1937).
HEINE, E. Handbuch der Kugelfunctionen. Vol. 2. Berlin, Reimer, 2nd ed. 1881, p. 1-31.
IGLISCH, R. Bemerkung uber die Trapezregel: Zusatz. Zeit. Angew. Math. Mech. 10, 616-618 (1930).
IRWIN, J. 0. On Quadrature and Cubature, or on Methods of Determining Approximately Single and Double
Integrals. Tracts for Computers, No. 10. London, Cambridge Univ. Press, 1923.
KL&GEL, G. S. Mathematisches Worterbuch. Vol. 4. Leipzig, Schwickert, 1823, p. 123-165.
KOWALEWSKI, A^ Newton, Cotes, Gauss, Jacobi. Vler grundlegende Abhandlungen uber Interpolation und
genaherte Quadratur. Leipzig, 1917, vi + 104 p.
KOWALEBSKI, G. Bemerkung fiber die Trapezregel. Zeit. Angew. Math. Mech. 10, 615-616 (1930).
KOWALEiBKI, G. Interpolation und genaherte Quadratur. Leipzig and Berlin, Teubner, 1932, v + 146 p.
LADEN » H. H. Fundamental polynomials of Lagrange interpolation and coefficients of mechanical
quadrature. Duke Math. Jour. 10, 145-151 (1943).
LENSE, J. Reihenentwicklungen in der mathematischen Physik. Berlin, de Gruyter, 1933, p. 107-113 .
LDJDOW, M. Numerische Infinitesimalrechnung. Berlin, Dummler, 1928, viii + 176 p., chap. 3.
n
L0SINSKT, S. Uber mechanische Quadraturen. (Russian. German summary.). Bull. Acad. Sci. URSS Ser.
Math. (Izvestia Akad. Nauk SSSR) 4, 113-126 (1940).
LOWAN, A. N^nd f^^^-^^J^^efficients in numerical integration formolae. Jour. Math.
I0WUJ, A. N., DAVIDS, N. and LEVENSON, A. Errata to "Table of the zeros of the Legendre polynomials
SLSfctt^oS wf m tUh f±CiBatB f ° r GaU88t BeChanlcal ^ adr ^ure formula". Bull.
MAJID, M. A^and CHAPMAN^ 8. n5 _^roxi»ate formulae for functions expressed as definite integrals.
MARKOFF, A. A. Differenzenrechrrang. Leipzig, Teubner, 1896, chap. 5, 9, 10.
MERRIFIELD, C. W. Report on the present state of knowledge of the application of quadratures and
interpolation to actual data. Brit. Assoc. Rep. for 1880, p. 321-378.
MnmraE ' Sk!-*«£w3: fSS3Sat&ff twmm ' (Ru * sian - *- ,ta * U " MI7<) ' ^ ACTd -
374
BIBLIOGRAPHY
MIKEIADZE, S, E, On formulas for mechanical cubatures, containing partial derivatives of the inte-
grand. Bull. Acad. Sci. Georgian SSR 4, 297-300 (1943).
VON MISES, R. Einfache Quadraturformel. Zeit. Angew. Math. Mech. 1, 73-74 (1921).
DE MONTESSUS, R. and D'ADHEMAR, R. Calcul numerique. Paris, Doin, 1911, 248 p., p. 139-237.
MOORS, B. P. Valeur approximative d'une integrale definie. Paris, Gauthier-Villars, 1905, vii + 195
p. and tables.
VON 0PP0IZER,T. Lehrbuch zur Bahribestimmung der Kometen und Planeten, vol.2. Leipzig,Engelmann, 1880,
vii + 635 p., P. 32-68.
PICONE, M. Lezioni di analisi infinitesiiaale. Catania, Circ. Mat. de Catania, 1923, vol. 1, part 2,
chap. 5, sec. 2, p. 564-602.
POLIA, G. Uber die Konvergenz von Quadraturverfahren. Math. Zeit. 37, 264-286 (1933).
RADAU, R. Etude sur les formules d' approximation qui servent a calculer la valeur numerique d'une
integral definie. Jour. Math. Pures et Appl. (3) 6, 283-336 (1880).
REMES* E, J. Sur certaines classes de fonctionelles lineaires dans les espaces C c et sur les termes
complementaires des formules d'analyse approximative. (Ukrainian. Russian and French summa-
ry.). Acad. Sci. RSS Ukraine. Rec. Trav. (Zbirnik Prace) Inst. Math., p. 47-82, 1940.
HEMES, E. J. Sur les termes complementaires de certaines formules d'analyse approximative. C. R.
(Doklady) Acad. Sci. URSS (N.S.) 26, 129-133 (1940).
SALZER, H. E. Coefficients for numerical integration with central differences. Phil. Mag. (7) 35,
262-264 (1944).
SCHELLBACH, C. H. Ueber mechanische Quadratur. (Programm, Berlin.). Berlin, Mayer and Miller, 1884.
SHOKAT, j # sur les quadratures mecaniques et sur les zeros des polynoraes de Tchebycheff dans un in-
tervalle infini. C. R. Acad. Sci. Paris 185, 597-598 (1927).
SHOHAT, J. and TAMARKIN, J. D. The Problem of Moments. Amer. Math. Soc. Mathematical Surveys,vol.
11, New York, Affler. Math. Soc., x94^, ■*-"-*■ + j^w p., CuSp. •+♦
STEFFENSEN, J. F. On the remainder term of certain formulas of mechanical quadrature. Skand. Akt-
uarietidskrift 4, 201-209 (1921).
STEFFENSEN, J. F. On a class of quadrature formulas. Proc. Intern. Math. Congr. Toronto, 1924, vol.
2. Toronto, Toronto Univ. Press, 1928, p. 837-844.
STEKLOV, 7» Sur 1* approximation des fonctions a 1'aide des polynomes de Tchebychef et sur les quadra-
tures. Bull. Acad. Imperiale Sci. (Izvestia Imperatorskoi Akademii Nauk.) (6) 11, 187-218,
535-566, 687-718 (1917).
rattrmrT tvrr tt -n 1 1 i.._ D.,11 A__J C_4 tS.oa ^%«.^U D«a.4j<>1/^! k'ij-nAamtA
Nauk.) (6) 12, 99-118 (1918).
STEKLOV, V. Quelques remarques complementaires sur les quadratures. Bull.Acad. Sci. Russ. (izvestia
Rossiiskoi Akademii Nauk.) (6) 12, 587-614 (1918).
STEKLOV, V. Sur les quadratures. Bull. Acad. Sci. Russ. (Izvestia Rossiiskoi Akademii Nauk.) (6):
12, 1859-1890 (1918); 13, 65-96 (1919).
STRANSKY, J. Bemerkung zum oberen Artikel. Aktuarske' Vedy 1, 61-62 (1930). See Tauber, A.
TADBER, A. Ueber ein Problem der Naherungsrechnung und die Makeham'schen Rentenwerte. Aktuarske' Vedy
1, 49-61 (1930).
THIELE, T. N. Interpolationsrechnung. Leipzig, Teubner, 1909, xii + 175 P., P» 21-28,
U3PEN3KY, J. V.
Amer. Math. Soc. 30, 542-559 (1928).
375
BIBLIOGRAPHY
VAHLEN, T. Konstruktionen und Approxiiaationen. Leipzig, Teubner, 1911, xii + 347 p., p. 206-214.
VERITY, E. R. Mathematics for Technical Students. London, Longmans, 1924, p. 419-433.
WALTHER, A. Zur numerischen Integration. Skand. Aktuarietidskrift 8, 148-162 (1925).
WALTHER, A. Beaerkungen uber das Tschebyscheff sche Verfahren zur numerischen Integration. Skand.
Aktuarietidskrift 13, 168-192 (1930).
KILLERS, F. A. Numerische Integration. Berlin, de Gruyter, 1923*
WINSTON, C. On mechanical quadrature formulae involving the classical orthogonal polynomials. Ann.
of Math. (2) 35, 658-677 (1934).
WOLFF, C. E. Note on numerical integration. Proc. Edin. Math. Soc. (2) 1, 139-148 (1928).
B. Functions of Several Variables
AITKEN, A. C. and FREWIN, G. L. The numerical evaluation of double integrals. Proc. Edin. Math. Soc.
42, 2-13 (1923-1924).
ARTMELADZE, N. uber Formeln der mechanischen Kubaturen. (Russian. German summary.). Trav. Inst.
Math. Tbilissi (Trudy Tbiliss. Mat. Inst.) 7, 147-160 (1940).
BIERMANN, 0. fiber naherungsweise Cubaturen. Monatsh. Math. Phys. 14, 211-225 (1903).
BIERMANN, 0. Zur naherungsweisen Quadratur und Cubatur. Monatsh. Math. Phys. 14, 226-242 (1903).
BURNSIDE, W. An approximate quadrature formula. Mess, of Math. (2) 37, 166-16? (I907-I908).
DAS GOPTA, P. N, On an interpolation formula connected with a definite integral in n-variables.
Bull. Calcutta Math. Soc. 33, 41-44 (1941).
SADOWSKY, M. A formula for approximate computation of a triple integral. Amer. Math. Month. 47,
539-543 (1940).
SHEPPARD, W. F. Central-difference formulae. Proc. Lond. Math. Soc. 31, 449-488 (1899).
SHEPPARD, W. F. Some quadrature-formulae. Proc. Lond. Math. Soc. 32, 258-277 (1900).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 1942, p. 374-375.
21. ORDINARY DIFFERENTIAL EQUATIONS
D'ADHEMAR, R. La balistique exterieure. Mem. Sci. Math. fasc. 65, 1934, 54 p.
ANDOYER, H. Sur la methods de Gauss pour le calcul des perturbations seculaires. C. R. Acad. Sci.
Paris 152, 418-420 (1918).
D'ASCIA, M. Saggio del metodo dei minimi quadrati per l'integrazione numerics delle equazioni
differenziali linear! . Rend. Accad. dei Lincei Roma (6) 11, 450-457 (1930).
BABAKOV, I. M. Zur Berechnung der hoheren Eigenfrequenzen der Drehschwingungen von reduzierter Welle.
(Russian. German summary.). Jour. Appl. Math. Mech. (Akad. Nauk SSSR.Zhurnal Prikl. Mat.
Mech.) 5, 109-124 (19U).
BABINI, J. Sobre la integracion aproximada de las ecuaciones diferenciales de segundo orden. Atti
Congr. Intern. Bologna 1928, vol. 3. Bologna, Zanichelli, 1930, p. 103-107.
376
BIBLIOGRAPHY
BALLANTINE. J. P. A numerical method of solving differential equations with a remainder. (Abstract),
Bull. Anter. Math. Soc. 32, 195-196 (1926).
BASHFORTH, F. and ADAMS, J. C. An Attempt to Test the Theories of Capillary Action... with an
Explanation of the Method of Integration Employed... Cambridge, Cambridge Univ.Press, 1883,
80 p. +59 p. tables, p. 15-62.
BATEMAN, K. Differential Equations. London, Longmans Green and Co., Longmans Modern Math. Series,
1918, chap. 11, p. 287-295.
BENDIXDN, I. Sur le calcul des integrales d'un systeme d' equations differentielles par des approxi-
mations successives. Stockh. Akad. Forh. 50, 599-612 (1893).
BENDIXDN, I. Sur les courbes dafinies par des equations differentielles. Acta Math. 24, 1-88 (1900).
BENNETT, A. A. Introduction to Ballistics. Washington, D. C, Govt. Printing Office, 1921.
acisnaaiif a. a. iaDj.eS ivr jXib&Txor doixioi>xcb« naoiuaig i<uu, ->. u., o.7«o*
BENNETT, A. A., MILNE, W. E. and BATEMAN, H. Numerical Integration of Differential Equations. Bull.
Nat. Res. Council No. 92, 1933, p. 51-87.
BICKLEY, W. G. A simple method for the numerical solution of differential equations. Phil. Mag. (7)
13, 1006-1114 (1932).
BICKLEY, W. G. Formulae for numerical differentiation. Math. Gaz. 25, 19-27 (1941).
BIEBERBACH, L. Bber neuere Lehrbucher der praktischen Analysis. Zeit. Angew, Math. Mech. 1, 61-67
(1921).
BIEBERBACH, L. Theorie der Differentialgleichungen. Berlin, Springer, 3rd ed. 1930, chap. 2, p. 27-
55.
BLISS, G. A. Functions of lines in ballistics. Trans. Amer. Math. Soc. 21,93-106 (1920).
, U. T. Von den freien Schwingungen eines Kreiselpendels bei endlichen Ausschlagen. Zeit.
Angew. Math. Mech. 20, 218-234 (1940).
B0UFFARD, J. Balistique exterieure. Nouvelle methode de calcul et d'etude de la trajeetoire d'un
projectile. Paris, Hermann et Cie, Actual. Sci. Ind., No. 907, 1942, 78 p.
BR3ST0W, L. Expansion theory associated with linear differential equations and their regular singu-
lar points. Trans. Amer. Math. Soc. 33, 455-474 (1931).
BRUN, ¥. Bber die Durchfuhrung der Eulerschen Differentiation bei Losung der Differentialgleichung
y' = f(x,y). 8 Skand. Math. Kongr. Stockholm 1934, (1935) p. 80-88.
BRUNS, E. H. Sber eine Differentialgleichung der Storungstheorie. Astr. Nachr. No. 2533, No. 2553,
1883.
BUCKNER, H. Uber eine Naherungslosung der gewohnlichen linear en Differentialgleichung 1. Ordnung.
Zeit. Angew. Math. Mech. 22, 143-152 (1942).
BURRAU, C. Recherches numeriques concernant des solutions periodiques d'un cas special du probleme
des trois corps. Astr. Nachr. No. 3230: 135, 233-240 (1894) J No. 3251: 136, 161-174 (1894).
BUSCHE, E. Zur Integration der ballistischen Hauptgleichung. Deutsche Math. 6, 97-99 (1941).
CALLANDREAU, 0. Sur une equation differentielle de la theorie des perturbations et remarques
relatives aux Nos. 2389 et 2435 des Astr. Nachr. Astr. Nachr. No. 2547 (1881).
CAQUE, J. Methode nouvelle pour I J integration des equations differentielles lineaires ne contenant
qu'une variable independante. Jour. Math. Pures Appl. (2) 9, 185-222 (1864).
377
BIBLIOGRAPHY
CAUCHT, A. L. Methods simple et generale pour la determination numerique des coefficients que
renferme le developpement de la fonction perturbatrice.Oeuvres completes d'Augustin Cauchy,
1st ser., vol. 5. Paris, Gauthier-Villars, 1885, p. 288-310.
CHADAJA, F. G. On the problem of numerical integration of ordinary differential equations. (Russian.
Georgian summary.). Bull, Acad. Sci. Georgian SSR 2, 601-608 (1941).
CHADAJA, F. G. On the error in the numerical integration of ordinary differential equations by the
method of finite differences. (Russian. Georgian summary.). Trav. Inst. Math. Tbilissi 11,
97-108 (1942). '
CHARBONNIER, P. Traite de balistique exterieure, vol. 2. Paris, Gauthier-Villars, 1927, 797 p., p.
691—786.
CHERRY, T. M. Integrals of systems of ordinary differential equations. Proc. Camb. Phil. Soc. 22.
273-281 (1924).
CLEMENTE, P. Maggiorazione dell'errore nel calcolo col metodo dei minimi quadrati della soluzione
periodica di una equazione differenziale, lineare, ordinaria,del secondo ordine. Rendiconti
Accad. dei Lincei Roma (6) 17, 262-264 (1933).
COLLATZ, L. Eine Verallgemeinerung des Differenzenverfahrens fur Differentialgleichungen. Zeit.
Angew. Math. Mech. 14, 350-351 (1934).
COLLATZ, L. Konvergenzbeweis und Fehlerabschatzung fur das Differenzenverfahren bei Eigenwertprob-
lemen gewohnlicher Differentialgleichungen zweiter und vierter Ordnune. Deutsche Math. 2.
189-215 (1937). *
COLLATZ, L. Schranken fur den ersten Eigenwert bei gewohnlichen Differentialgleichungen zweiter
Ordnung. Ing. Arch. 8, 325-331 (1937).
COLLATZ, L. Genaherte Berechnung von Eigenwerten. Zeit. Angew. Math. Mech. 19, 224-249, 297-318
\1939 ) •
COLLATZ, L. Naturliche SchriUweite bei numerischer Integration von Differentialgleichungssystemen.
Zeit. Angew. Math. Mech. 22, 216-225 (1942).
COLLATZ, L. and ZURMOhL, R. Beitrage zu den Interpolationsverfahren der numerischen Integration von
Differentialgleichungen 1. und 2. Ordnung. Zeit. Angew. Math. Mech. 22, 42-55 (1942).
COLLATZ, L. and ZURM&HL, R. Zur Genauigkeit verschiedener Integrationsverfahren bei gewohnlichen
Differentialgleichungen. Ing. Arch. 13, 34-36 (1942).
CORIOLIS, G. Memoire sur le degre d'approximation. . . Jour. Math. Pures Appl. 2, 229-244 (1837).
COTTON, E. Sur 1 'integration approchee des equations differentielles. Bull. Soc. Math. France 36,
225—246 (1908).
COTTON, E. Sur 1 'integration approchee des equations differentielles. Acta Math. 31, 107-126 (1908).
COTTON, E. Approximations successives et equations differentielles. Paris. Gauthier-Villars. Mem.
Sci. Math. fasc. 28, 1928, 47 p. *
DARWIN, G. H. Periodic orbits. Acta Math. 21, 99-242, espec. 118 ff. (1897).
DEDERICK, L. S. The mathematics of exterior ballistics computations. Amer. Math. Month. 47, 628-
DUFFING, G. Zur numerischen Integration gewohnlicher Differentialgleichungen. Forschungsarbeiten
auf dem Gebiete des Ingenieurwesens 224, 29-50 (1920).
EULER, L. ^gstitutionum calculi integralis, vol. 1. St. Petersburg (Leningrad), 1768, 542 p., p.
FALKNER, v - «• A method of numerical solution of differential equations. Phil. Mag. (7)21, 624-640
378
BIBLIOGRAPHY
FANTA, W. fiber die angenaherte Auflosung von gewohnlichen Differentialgleichungen und Anwendung
auf Probleme der Mechanik. (Berlin Diss.). Vienna, Carl Gerold's Sohn, 1931, 40 p.
FEINSTEIN, L. and SCHWARZSCHILD, M. Automatic integration of linear second-order differential
equations by means of punched card machines. Rev. Sci. Instr. 12, 405-408 (1941).
FORD, L. R. The numerical integration of differential equations (abstract). Bull. Amer. Math. Soc.
30, 215 (1924).
FORSYTH, A. R. Treatise on Differential Equations. London, Macmillan, 6th ed. 1929, p. 53-56.
FOWLER, R. H., GALLOP, E. G., LOCK, C. N. and RICHMOND, H. W. The aerodynamics of a spinning shell.
Phil. Trans. Roy. Soc. Lond. A221, 295-387 (1920).
FRAZER, R. A., JONES, W. P. and SKAN, S. W. Note on approximations to functions and to solutions
of differential equations. Phil. Mag. (7) 25, 740-746 (1938).
FUBINI G. An elemental*^ observation of the equations of external ballistics- (Spanish). Math.
*Notae 2, 3-10 (1942).
FUNK, P. Ueber Duffings Methode sur nussrischer. Integration von gewohnlichen Differentialgleichungen.
Zelt* Angew, Math, Mech, 7, 410-411 (1927).
GAJAS, M. La comparaison des integrales success! ves de M. Picard avec 1' integral cherchee. Bull.
Sci. Math. (2) 58, 236-240 (1934).
GARCIA, G. Mouvement des projectiles autour de son centre de gravite. Sur le mouvement gyroscopique;
mouvement pendulaire des projectiles; derivation. Revista Ci. Lima 42, 541-685 (1940).
GAU, E. Sur un theoreme de M. E. Picard. Bull. Soc. Math. France 43, 62-69 (1915).
GEBELEIN, H. Zur praktischen Losung gewohnlicher Differentialgleichungen mittels schrittweiser
Annaherung. Zeit. Angew. Math. Mech. 13, 385-386 (1933).
GOLAB, S. Dn theoreme de la theorie des equations differentielles approchees. Mathematica (Cluj)
16* 61-65 (1940) ?
GOORSAT, E. Cours d'analyse mathematique, vol. 2. Paris, Gauthier-Villars, 5th ed. 1933, 685 p.,
p. 384-402.
GRAMMEL, R. Ein Beitrag zur Losung des Dreikorperproblems. Astronomical Papers dedicated to Elis
Stromgren, Copenhagen, Einar Munksgaard, 1940, p. 40-50.
GRQENE7ELD J. Muserische Integration der Hauptgleichung der ausseran Ballistik- Zeit- Angew. Math,
Mech. 7, 150-151 (1927).
GRONWALL, T. H. Qualitative properties of the ballistic trajectory. Ann. of Math. (2)22, 44-65(1920).
HADAMARD, J. Cours d'analyse, vol. 2. Paris, Hermann, 1930,721 p., p. 297-313.
HARTREE, D. R. Ballistic calculations. Nature 106, 152-154 (1921).
HARTREE, D. R. On an equation occurring in Falkner and Skan's approximate treatment of the equations
of the boundary layer. Proc. Camb. Phil. Soc. 33, 223-239 (1937).
HERMANN, E. E. Exterior Ballistics, 1935. Annapolis, U. S. Naval Inst., reprint 1940, viii + 305 p.
HILL, G. W. Researches in the lunar theory. Amer. Jour. Math. 1, 5-26, 129-147, 245-260 (1878).
HIRSCHFELD, H. 0. A generalization of Picard 1 s method of successive approximation. Proc. Camb. Phil.
Soc. 32, 86-95 (1936).
HORNSTEIN, M. „ Einige Bemerkungen uber lineare Differenzengleichungen zweiter Ordnung und liber
fcetienDrucne. nee. aatn. \ubx,, oognim; n,o» p \nu» «r'oo \i-mf
379
BIBLIOGRAPHY
HORT, W. Die Differentialgleichungen des Ingenieurs. Berlin, Springer, 2nd ed. 1925, xLi + 700 p.,
p. 216-325.
IGLISCH, R. Zur praktischen Behandlung von Randwertaufgaben gewohnlicher linearer Differential-
gleichungen mit nicht konstanten Koeffizienten. Zeit. Angew. Math. Mech. 14, 51-58 (1934).
DICE, E. L. Ordinary Differential Equations. London, Longmans, 1927» p. 540-547.
INFELD, L. On a new treatment of some eigenvalue problems. Phys. Rev. (2) 59, 737-747 (1941).
JACKSON, D. The method of numerical integration in exterior ballistics. War Department document
No. 984. Washington, D. C, Govt. Printing Office, 1921, 43 p.
KANTOROVrrCH, L. The method of successive approximations for functional equations. Acta Math. 71,
63-97 (1939).
KELLER, E. G. Beat theory of non-linear circuits. Jour. Franklin Inst. 228, 319-337 (1939).
KLOSE, A. Zur Integration der ballistischen Gleichung. Deutsche Math. 2, 473-479 (1937).
KNOBLOCH, H. Zur Interpolation von Kurvenscharen. Zeit. Angew. Math. Mech. 22, 364-366 (1942).
KORMES, M. A note on the integration of linear second-order differential equations by means of punch-
ed cards. Rev. Sci. Instr. 14, 118 (1943).
KORN, A. Uber eine Methode der sukzessiven Naherungen zur Losung linearer gewohnlicher und partieller
Differentialgleichungen. Sitzber. Berl. Math. Ges. 15, 115-119 (1916).
KRAWTCHOUK, M. Sur la methode de N. Kryloff pour 1' integration approchee des equations de la physique
mathematique. C. R. Acad. Sci. Paris 183, 474-476 (1926).
KRAWTCHOUK, M. On a method of N. Kryloff for the integration of ordinary differential equations.
(Ukrainian). Mem. Acad. Sci. Kiev (2) 5, 12-33 (1927).
KRAWTCHOUK, M. Sur l'integration approche"e des equations differentielles lineaires. Atti Congr.
Intern. Bologna 1928, vol. 3, Bologna, Zanichelli, 1930, p. 109-115.
KRAWTCHOUK, M. Sur les derivees des integrales approchees de certaines equations differentielles.
Rend. Circ. Mat. Palermo 54, 194-198 (1930).
KRYLOFF, N. Les methodes de solution approchee des problemes de la physique mathematique. MenuSci.
Math., fasc. 49. Paris, Gauthier-Villars, 1931, 70 p.
KRYLOFF, N. Sur la solution approchee des problemes de la physique mathematique et de la science
d'ingehieur. Bull. Acad. Sci. URSS Leningrad (Izvestia Akad. Nauk SSSR) (7) 1930, 1089-1114
(1930). Reprint Revista Mat. Hisp. Amer. (2) 6, 213-238 (1931).
KRYLOFF, N. and BOGOLIUBOFF, N. Upon some new results in the domain of non-linear mechanics.
Proc. Indian Acad. Sci. A 3, 523-526 (1936).
KRYLOFF, N. and BOGOLIUBOFF, N. Introduction to Non-Linear Mechanics. (Tr. Lefschetz, S.). Annals of
Mathematics Studies, No. 11. Princeton, N. J., Princeton Univ. Press, 1943.
KUTTA, W. Beitrag zur naherungsweisen Integration totaler Differentialgleichungen. Zeit. Math. Phys.
46, 435-453 (1901).
LAGRANGE, J. L. Essai sur le probleme des trois corps. Oeuvres de Lagrange, vol. 6. Paris, Gauthier-
Villars, 1873, p. 227-331.
LAHAYE, E. Une methode nouvelle d'integration de certains groupes d'equations differentielles.
C. R. Acad. Sci. Paris 185, 172-173 (1927).
LAHAYE, E. Les iterations integrales convergentes. Application aux equations differentielles.
du premier ordre algebriques en y et dy/dx. Acad. Roy. Belgique, CI. Sci. Mem. Coll. 18,
No. 5, 1939, 65 p.
380
BIBLIOGRAPHY
LAHAYE, E. Les iterations integrales convergentes et leur application aux equations differentielles
du premier ordre, algebriques en y et y 1 . C. R. Acad. Sci. Paris 210, 621-624 (1940).
LAHAYE, E. Sur la resolution des equations dz/dx * r(x,z)(r rationnel en z) par des iterations inte^
grales et differentielles convergentes. Jour. Math. Pures Appl. (9) 22, 1-23 (1943).
LANCZOS, C. A new approximation method in solving linear differential equations with non-oscillating
coefficients. (Abstract). Bull. Amer. Math. Soc. 41, 183-184 (1935).
LANCZOS, C. A new approximation method in solving linear differential equations with rational
coefficients. (Abstract). Bull. Amer. Math. Soc. 42, 30 (1936).
LAURTTZEN, S. Nogle Bemaerkninger om Diffrentialligningen dy/dx = f(x,y). Mat. Tidsskr. B, K0ben-
havn 1937, 104-108 (1937).
LEGENDRE, A. M. Dissertation sur la question de balistique proposee par l'Academie Royale des
Sciences et Belles-Lettres de Prusse pour le prix de 1782. Berlin, G. J. Decker,1782, 68p.
LEVY, H. The numerical solution of a certain class of differential equations. Proc. Lond. Math.
Soc. (2) 24, 459-470 (1926).
LEVY- K« A nussrical stu^ of differsitial equations Jour Lc
LEVY, H. and BAGG0TT, E. A. Numerical Studies in Differential Equations, vol. 1. London, Watts,
1934, viii + 238 p.
LIAP0UN0FF, A. M. Sur une serie dans la thebrie des equations differentielles lineaires de second
ordre a coefficients periodiques. Mem. Acad. St. Petersbourg (8) 13, No. 2, 70 p. (1902).
LINDELOF, E. Sur l'application des methodes d' approximations successives a 1' etude des int£-
grales reelles des equations differentielles. Jour .Math. Pures Appl. (4) 10, 117-128 (1894).
LINDELOF, E. Remarques sur 1' integration numerique des equations differentielles ordinaires. Acta
Soc. Sci. Fennicae A(2) 2, No. 13, 21 p. (1938).
T T*mRTT!TYP A Ba-t4-<M>~ nn T»»«»Mf<.> A*,-~ rv« ##«.«»_a-< „ 1 _T «i _u.. J__ wO_ .11 1- \t a i
St. Petersbourg (7) 31, No. 4, 20 p. (1883).
LiDUVULE, J. Sur le developpement des fonctions ou parties de fonctions en series dont les di-
vers termes sont assujettis a satisfaire a une meme equation differentielle du second ordre
contenant une parametre variable. Jour. Math. Pures Appl. 2, 16-22 (1837).
LIOUVILLE, J. Sur la thebrie des equations differentielles lineaires et sur les developpements des
fonctions en series. Jour. Math. Pures Appl. 3, 561-614 (1838).
LIPSCHITZ, R, Sur la possibilite' d ' integrer completement un systeme donne d'equations different-
ielles. Bull. Sci. Math. 10, 149-159 (1876).
LIPSCHITZ, R. Lehrbuch der Analysis, vol. 2. Bonn, Cohen, 1880, xiv +■ 734 p., p. 500-512.
MADELUNG, E. Dber eine Methode zur schnellen numerischen Losung von Diff erentialgleichungen
zweiter Ordnung. Zeit. Phys. 67, 516-518 (1931).
MADER, K. Mathematische Hilfsmittel in der Physik. (Vol. Ill of Handbuch der Physik). Berlin,
Springer, 1928, chap. 15, p. 631-635.
MARCHANT METHODS. Starting values for Milne-method integration of ordinary differential equations
of first order, or of second order when first derivatives are absent. The method of
Taylor's series. MM-261, Oct. 1943, 4 p. Marchant Calc. Mach. Co., Oakland, Calif.
MARCHANT METHODS. Starting value for Milne-method integration of ordinary differential equations
of the first order. The method of Milne. MM-260, Jan., 1944, H p.
381
BIBLIOGRAPHY
MARCHANT METHODS. Milne method of step-by-step double integration of second order differential
equations in which first derivatives are absent. MM-216A, Jan., 1943, 6 p.
MARCHANT METHODS. Milne method of step-by-step integration of ordinary differential equations when
starting values are known. MM-216, June, 1942, 10 p.
MASSERA, J. F. Formulae for finite differences with applications to the approximate integration of
differential equations of the first order. (Spanish). Publ. Inst. Mat. Univ. Nac. Litoral
4, 99-166 (1943).
McEWEN, W. H. Problems of closest approximation connected with the solution of linear differential
equations. Trans. Amer. Math. Soc. 33, 979-997 (1931).
McEWEN, W. H. On the approximate solution of linear differential equations with boundary conditions.
Bull. Amer. Math. Soc. 38, 887-894 (1932).
MIKELADZE, S. Uber die Integration von Differentialgleichungen mit Hilfe der Differenzenmethode.
(Russian. German summary.). Bull. Acad. Sci. URSS Ser. Math. (Izvestia Akad. Nauk SSSR)
1939, 627-642 (1939).
MIKEIADZE, S, Verallgemeinerung der Methode der numerischen Integration von Differentialgleichungen
mit Hilfe der Formeln der mechanischen Quadra tur. (Russian. German summary.). Trav. Inst.
Math. Tbilissi (Trudy Tbiliss. Mat. Inst.) 7, 47-63 (1940).
MIKELADZE, S. On the approximate integration of linear differential equations with discontinuous
coefficients. (Russian.). Bull. Acad. Sci. Georgian SSR 3, 633-639 (1942).
MIKELADZE, S. New formulas for the numerical integration of differential equations. (Russian.).
Bull. Acad. Sci. Georgian SSR 4, 215-218 (1943).
MILNE, W. E. Numerical integration of ordinary differential equations. Amer. Math. Month. 33.
455-460 (1926). '
MILNE, W. E. On the numerical solution of a boundary value problem. Amer. Math. Month. 38, 14-17
(1931).
MILNE, W. E. On thQ. numerical integration of certain differential equations of the second order.
Amer. Math. Month. 40, 322-327 (1933).
MILNE, W. E. The numerical integration of y» « + g(x)y = f(x). Amer. Math. Month. 49, 96-98 (1942).
MIRANDA, C. Teorend e metodi per l'integrazione numerica della equazione differenziale di Fermi.
Memorie Reale Accad. d' Italia 5, 285-322 (1934).
VON MISES, R. Zur numerischen Integration von Differentialgleichungen. Zeit. Angew. Math. Mech.
10, 81-92 (1930).
MOIGNO, F. N. M. Leqons de calcul differentiel et de calcul integral, vol. 2. Paris. Bachelier. 1844
xlviii + 783 p., p. 385-434, 513-534. ' '
DE MONTESSUS, R. and D'ADHEMAR, R. Calcul numerique. Paris, Doin, 1911, 249 p., p. 139-237.
M00LT0N, F. R. Periodic Orbits. Washington, D. C, Carnegie Institution, 1920, xiii + 524 p.
MODLTON, F. R. Numerical solution of differential equations. Chap. X of Smithsonian mathematical
formulae and tables of elliptic functions. (Edited Adams, E. P. and Hippisley, R. L.).
Smithsonian Miscellaneous Collections 74, No. 1, 220-242 (1922).
MOULTON, F. R. Differential Equations. New York, Macmillan, 1930, p. 179-231.
MOULTON, F. R. New Methods in Exterior Ballistics. Chicago, Univ. Chicago Press, 1926.
MULLER, M. Ueber die Eindeutigkeit der Integrale eines Systems gewohnlicher Differentialgleichungen
und die Konvergenz einer Gattung von Verfahren zur Approximation dieser Integrale. Sitzber.
Heidelberg, 1927 (9 Abb..), 38 p.
382
BIBLIOGRAPHY
M&LLER, M. fiber das Fundamental-theorem in der Theorie der gewohnlichen Differentialgleichungen.
Math. Zeit. 26, 619-645 (1927).
M&LLER, M. fiber den Konvergenzbereich des Verfahrens der schrittweisen Naherungen bei gewohnlicher
Differentialgleichungen. Math. Zeit. 41, 163-175 (1936).
M&LLER, M. fiber die Existenz periodischer Losungen bei gewissen Systemen gewohnlicher Diff eren-
tialgeleichungen erster Ordnung. Math. Zeit, 48, 128-135 (1942) «
NAGUMO, M. fiber das Verfahren der sukzessiven Approximationen zur Integration gewohnlicher Differ-
entialgleichung und die Eindeutigkeit ihrer Integrale. Jap. Jour. Math. 7, 143-160 (1930).
NAGUMO, M. fiber das Verhalten der Integrale vonAy" ■+- f(x,y,y', X ) = fur A -» 0. Proc. Phys.-
Math. Soc. Japan 21, 529-534 (1939).
NASTA, M. Contributo al calcolo delle velocita critiche degli alberi motori. Rend. Accad. dei Lincei
Roma (6) 12, 209-216 (1930).
NIEMYTZKI, V. Integration qualitative approximative du systeme d'equations dx/dt s Q(x,y), dy/dt =
P(x,y). C. R. (Doklady) Acad. Sci. URSS (N. S.) 38, 62-65 (1943).
wvnma&o v ra „ -!_*.4«-.u* S^Ah.h. Am*> .Isww.Hr.ssnenHal iinoar, . Got*-- Haehr. 1<?19. "373-391*
NOWAKOflSKI, A. Zur numerischen Integration gewohnlicher Differentialgleichungen mit der Rechenma-
schine. Zeit. Angew. Math. Mech. 13, 299-322 (1933).
NUMEROV, B. Note on the numerical integration of d x/dt = f(x,t). Astr. Nachr. 230, 359-364
(1927).
NYSTR&M, E. J. fiber die numerische Integration von Differentialgleichungen. Acta Soc. Sci. Fennicae
50, No. 13, 56 p. (1925).
0KAMURA, H. Sur 1* approximation successive et l'unicite de la solution de dy/dx s f(x,y). Memoirs
Coll. Sci. Kyoto Imperial Univ. 14, 85-96 (1931).
schitz. Bull. Soc. Math. France 27, 149-152 (1899).
PAINLEVE, P. Gewohnliehe Differentialgleichungen; Existenz der Losungen. Ency. Math. Wiss., vol.
II 1, lj article II A 4a. Leipzig, Teubner, 1900, p. 189-229.
PEAN0, G. Integration par series des equations differentielles lineaires. Math. Ann. 32, 450-456
(1888).
PERES, J. Sur la methode des fonctions majorantes et la methode des approximations successives.
Bull. Sci. Math. (2) 39, 179-181 (1915).
PETROVITCH, M. Integration qualitative des equations differentielles. Mem. Sci. Math, fasc.46.
Paris. Gauthier-Villars, 1931, 58 p.
PIAGGI0, H. T. H. An Elementary Treatise on Differential Equations and Their Applications. London,
Bell, 2nd ed. 1928, p. 94-108, 224-228.
PIAGGI0, H. T. H. On the numerical integration of differential equations. Phil. Mag. (6) 37, 596-
600 (1919).
PICARD, E, Memoire sur la theorie des equations aux derivees partielles et la methode des approxi-
mations successives. Jour. Math. Pures Appl. (4) 6, 145-210, 231 (1890).
PICARD, E. Sur l'application des methodes d» approximations successives a 1' etude de certaines
equations differentielles ordinaires. Jour. Math. Pures Appl. (4) 9, 217-271 (1893).
PICARD, E. Traite d*analyse. Paris, Gauthier-Villars: vol. 2, 3rd ed. 1926, p. 368-394; vol.3, 3rd
ed. 1928, p. 88-99.
383
BIBLIOGRAPHY
PICONE, If, Sul metodo delle n d n i me potenze ponderate e sul metodo di Ritz per il calcolo approssimato
nei problem! della fisica-matematica. Rend. Circ. Mat. Palermo 52, 225-253 (1928).
PICONE, M. Maggiorazione dell'errore d'approssimazione nel metodo d'integrazione Cauchy-Lipschitz
del sistemi di equazioni differenziali ordinarie. Rend. Accad. Lincei Roma (6) 15. 859-864
(1932).
POINCARE, H. Les meihodes nouvelles de la mecanique celeste, vol. 1. Pails, Gauthier-Villars, 1892,
385 p.
POMET, L. Sur le theoreme d'existence, etc. C. R. Acad. Sci. Paris 180-569-571, 725-727. 1093-1096.
2006-2008 (1925).
POPOFF, K. Ueber elne Eigenschaft der ballistischen Kurve und ihre Anwendung auf die Integration
der Bewegungsgleichungen. Zeit. Angew. Math. Mech. 1, 96-106 (1921).
POPOFF, K. Les methodes d« integration de Poincare et le probleme geherale de la balistique ex-
terieure. Paris, Gauthier-Villars, 1925, 76 p.
PORTER, M. B. On the roots of functions connected by a linear recurrent relation of the second
order. Ann. of Math. (2) 3, 55-70 (1902).
PUGACHEV, V. S. Notes on exterior ballistics of projectiles and bombs. (Russian. English summary.).
Appl. Math. Mech. (Akad. Nauk SSSR. Prikl. Mat. Mech.) 6, 347-368 (1942).
PUGACHEV, V. S. Approximate method of solving the non-linear problem of a rotating projectile.
(Russian. English summary.). Appl. Math. Mech. (Akad. Nauk SSSR. Prikl. Mat. Mech.) 7. 313-
324 (1943). *»->*-
RANKIN, A. W. On the average-slope method of solving differential equations. Amer. Math. Month. 45.
461-462 (1938). '
RATZERDORFER, J, Determination of the buckling load of struts with successive approximation. Jour.
Roy. Aeronaut. Soc. 47, 103-105 (1943).
REMES, E. Some approximate formulae for the numerical integration of differential equations. Phil.
Mag. (7) 5, 392-400 (1928).
RICHARDSON, L. F. How to solve differential equations approximately by arithmetic. Math. Gaz. 12.
415-421 (1925). '
RIEBESELL,P. Uber die Integration der ballistischen Hauptgleichung bei Andwendung des Soramerfeldschen
Luftwiderstandsgesetzes. Arch. Math. Phys. (3) 25, 103-108 (1916).
ROOT, R. E. The Mathematics of Engineering. Baltimore, Williams and Wilkins, 1927, p. 514-528.
RUNGE, C. Ueber die numerische Auflosung von Differentialgleichungen. Math. Ann. 46, 167-178 (1895).
RUNGE, C. and WILLERS, F. A. Numerische und graphische Quadratur und Integration gewohnlicher und
partieller Differentialgleichungen. Ency. Math. Tttss., vol. II 3, 1; article II C2.Leipzig,
Teubner, 1915, p. 47-176.
VON SANDEN, H. Zur Berechnung des kleinsten Eigenwerts von y» + "X p(x)y - 0. Zeit. Ancew. Math.
Mech. 21, 381-382 (1941).
SAUER, R. Uber Interpolation von Kurvenscharen mit Anwendung auf die Berechnung von Geschossflug-
bahnen. Zeit. Angew. Math. Mech. 20, 280-284 (1940).
SAUER, R. and POSCH, H. Anwendungen des Adamsschen Integrationsverfahrens in der Ballistik. Ine.
Arch. 12, 158-168 (1941).
SCARBOROUGH, J. B. Numerical Mathematical Analysis. Baltimore, Johns Hopkins Press, 1930, p. 218-283.
SCHEFFE, H. Linear differential equations with two-term recurrence formulas. Jour. Math. Phys. (M.
I.T.) 21, 240-249 (1942).
384
BIBLIOGRAPHY
SnHELKUNQFF, S. A, Solution of linear and slightly nonlinear differential equations. Quart. Appl.
Math. 3, 348-355 (1%6).
SCHULZ, G. Interpolationsverfahren zur numerischen Integration gewohnlicher Differentialgleichungen.
Zeit. Angew. Math. Mech. 12, 44-59 (1932).
SCHULZ, G. Fehlerabschatzung fur das Stormersche Integrationsverfahren. Zeit. Angew. Math. Mech. 14,
224-234 (1934).
SEVERINI, C. Sull'integrazione approssimata delle equazioni differenziali ordinarie. Bologna, Zan-
ichelli, 1899, 27 p.
SHOHAT, J. A new analytical method for solving van der Pol's and certain related types of non-linear
differential equations, homogeneous and non-homogeneous. Jour .Appl. Phys. 14, 40-48 (1943).
SHOHAT, J. On van der Pol's and non-linear differential equations. Jour. Appl. Phys. 15, 568-574
(1944).
SOUTHWELL, R. V. On the natural frequencies of vibrating systems. Proc. Roy. Soc. Lond. 174A, 433-
457 (1940).
<5«n»»jfr£ v gur Berechnunc einer Flusbahnschar nach dem Athenschen Verfahren. Zeit. Angew. Math.
" '"' " *Mech. 20, 350-357 (1940).
STEFFENSEN, J. F. On the degree of rigour required in numerical integrations. 5 Kongr.Skand. Math,
in Helsingfors, p. 125-130, 1922.
STEKLOFF W. Sur les problemes de representations des fonctions a l'aide de polynomes, du calcul
approche des integrales definies, du developpement des fonctions en series infinies suivant
les polynomes et de 1' interpolation, considerees au point de vue des idees de Tchebycheff.
Proc. Intern. Math. Congr. Toronto, 1924, vol. 1, 1928, p. 631-640.
ST0HLER, K. Eine Vereinfachung bei der numerischen Integration gewohnlicher Differentialgleichungen.
Zeit. Angew. Math. Mech. 23, 120-122 (1943).
STDRMER. C. Sur les tra.lectoires des corpuscules electrises dans 1'espace sous 1* action du magnet-
isme terrestre avee application aux aurores boreales. Arch. Sci. Phys. Nat. Geneve (4) 2h,
5-18, 113-158, 221-247 (1907).
ST6RMER, C. Resultats des calculs numeriques des trajectoires des corpuscules electriques dans le
champ d'un aimant elementaire. Videnskapsselskapets Skrifter, Kristiania 1913: 1, No.4, 74
p.; 2, No. 10, 58 p. J 2, No. 14, 64 p. (1913).
St6rMER, G* Melhode d» integral ion numerique des equations differentielles ordinaires. C. R. Congr.
Intern. Math. Strasbourg 1920. Toulouse, Privat, 1921, p. 243-257.
STRUTT, M. J. 0. Der charakteristische Exponent der Hillschen Differentialgleichung. Math. Ann.
im ccn_cJlQ fioo«^
__.. .. — *t_ t__1 J_J. JL* _i> JJX>i> i<-1 An ..~4-4 A -.« ^Dnc^an P*»amAVt eiinn!i<nr '\ Till 11
Univ.. Tashkent 16, 273-286 (1927).
TA LI. Uber die allgemeine lineare Differentialgleichung. Comnent. Math. Helv. 12, 1-19 (1939-1940).
TAMARKINE, J. D. Sur la methode de C. Stormer pour 1' integration approchee des equations different-
ielles ordinaires. Math. Zeit. 16, 214-219 (1923).
TAMBS LYCHE, R. Solution explicite de l'equation differentielle generale du premier ordre. Avhandl.
25-Arsjubileet Tekniske H^iskole Trondheim, 1935, p. 765-786. Reprint Det Kgl.Norske Viden-
skabers Selskabs Skrifter, Trondheim 1935, (2), No. 35, 24 p. (1935).
T0LLMIEN, W. Ober die Fehlerabschatzung beim Adamsschen Verfahren zur Integration gewohnlicher
Differentialgleichungen. Zeit. Angew. Math. Mech. 18, 83-90 (1938).
TSCHAPPAT, W. H. Ballistics. Encyclopaedia Britannica, New Volumes 30, 386-394 (1922).
385
BIBLIOGRAPHY
TORTON, F. J. The errors in the numerical solution of differential equations. Phil. Mag. (7) 28, 359-
363 (1939).
TURTON, F. J. Two notes on the numerical solution of differential equations. Phil. Mag. (7) 28,
381-3*4 (1939).
VAHLEN, T. Beitrage zur Ballistik. Arch. Math. Phys. (3): 25, 209-231 (1916); 26, 119-125 (1917).
VD2T0RIS, L. Sber die Integration gewohnlicher Differentialgleichungen durch Iteration. Monatsh.
Math. Phys.:39, 15-50 (1932); 41, 3*4-391 (1934).
WAR DEPARTMENT, UNITED STATES OF AMERICA. A Course in Exterior Ballistics. War Dept. document No.
1051. Washington, D. C, Govt. Printing Office, 1921, 127 P.
WEBSTER, A. G. On the Springfield rifle and the Leduc formula. Proc. Nat. Acad. Sci. U.S.A. 6, 289
(1920).
WEINEL, E. Eine Erweiterung des Grammelschen Verfahrens zur Berechnung von Eigenwerten und Eigen-
funktionen. Ing. Arch. 10, 283-291 (1939).
WEIL, H. Concerning the differential equations of some boundary-layer problems. Proc. Nat. Acad. Sci.
U.S.A.: 27, 578-583 (1941); 28, 100-102 (1942).
WEIL, H. On the differential equations of the simplest boundary-layer problems. Ann. of Math. (2) 43,
381-407 (1942).
WHITEHEAD, A. N. Graphical solution for high-angle fire. Proc. Roy. Soc. Lond. A94, 301-307 (1917-
1918).
WIENER, 0. Die streckenweise Berechnung der Geschossflugbahnen. Abh. Ges. Wiss. Leipzig 36, No. 1, 66
p., (1918).
WILLERS, F. A. Methoden der praktischen Analysis. Berlin, de Gruyter, 1928, 344 p., p. 305-334.
ZAREMBA, S. K. Remarques sur I 1 integration approchee des equations differentielles. Bull. Intern.
Acad. Polon. Sci. Lett., CI. Sci. Math. Nat. A 1936, 528-535 (1937).
ZECH, T. Anschauliches zur Picarditeration der Differentialgleichungen. Zeit. Angew. Math. Mech.
17, 341-352 (1937).
ZECH, T. Zum Abklingen nichtlinearer Schwingungen. Ing. Arch. 13, 21-33 (1942).
ZURMUHL, R. Zur numerischen Integration gewohnlicher Differentialgleichungen zweiter und hoherer
Ordnung. Untersuchungen zu den Verfahren von Blaess und Runge-Kutta-Nystrom. Zeit. Angew.
Math. Mech. 20, 104-116 (1940).
22. PARTIAL DIFFERENTIAL EQUATIONS
ALLEN, D. N., SOUTHWELL, R. V. and VAISET, G. Relaxation methods applied to engineering problems.
XI. Problems governed by the "quasi-plane-potential equation". Proc. Roy. Soc. Lond. 183A,
258-283 (1945).
ARTEMIEFF, N. Die Anwendung des Storungsverfahrens zur Berechnung der Eigenwerte bei Deformation des
Randes. Rec. Math. Moscow (Mat. Sbornik) 39, No. 3, 52-66 (1932).
BATEMAN, H. Partial Differential Equations. Cambridge, Cambridge Univ. Press, 1932,xii + 522 p., p.
76, 144-152.
BENNETT, A. A., MILNE, W. E. and BATEMAN, H. Numerical integration of differential equations. Report
of committee on numerical integration. Bull. Nat. Res. Council, No. 92. Washington, D. C,
Nat. Acad. Sci., 1933, chap. 4.
386
BIBLIOGRAPHY
BERGMANN, S. Uber die Entwicklung der harmonischen Funktionen der Ebene und des Raumes nach Orthog-
onaifunktionen. Math* Ann. 86, 238-271 (1922).
BERGMANN, 8. Ein Naherungsverfahren zur Losung gewisser partieiier, linearer Differentialgleichungen.
Zeit. Angew. Math. Mech. 11, 323-330 (1931).
BERGMANN, S. Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen
I. C. R. (Doklady) Acad. Sci. URSS. (N.S.) 15, 227-230 (1937).
BERGMAN, S. The approximation of functions satisfying a linear partial differential equation. Duke
Math. Jour. 6, 537-561 (1940).
BICKIEY, W. G. Experiments in approximating to solutions of a partial differential equation. Phil.
Mag. (7) 32, 50-66 (1941).
B3EZEN0, C. B. and GRAMMEL, R. Technische Dynamik. Berlin, Springer, 1939 (Reprint, Ann Arbor, Ed-
wards, 1944) p. 135-180.
ft If M ...
BINDER, L. Uber Warmeubergang auf ruhige Oder bewegte Lufte sowie Luftung uhd Kuhlung elektrischer
Maschinen. Halle, Knapp, 1911, v + 112 p., p. 20-26.
BIRKH0FF, G. E. Circular plates of variable thickness. Phil Mag. (6) 43, 953-962 (1922).
BLAISDELL, B. E. The physical properties of fluid interfaces of large radius of curvature. Jour.
Math. Phys. (M.I.T.) 19, 186-245 (1940).
B0UKIDIS, N. A. and RUGGTER0, R. J. An iterative method for determining dynamic deflections and
frequencies. Jour. Aeronaut. Sci. 11, 319-328 (1944).
BOUSSINESQ, J. Sur le calcul de plus en plus approche" des vit esses bien continues de regime
uniforme par des polynomes, dans un tube prismatique a section carree. C. R. Acad. Sci.
Paris 158, 1743-1749 (1914).
BREMEKAMP, H. Quelques applications de la methode des approximations success! ves. Proc. Akad. Wet.
Amsterdam 41, 291-300 (1938).
BRILLOUIN, it. La methode des iooindres Carres ei less equations aux derivees pariiellea de la physique
mathematique. Ann. de Phys. 6, 137-233 (1916).
BR00WER, F. Wellenmechanische Eigenwertprobleme und Integration durch Reihen, Ann. der Phys. 84,
915-929 (1927).
CARMICHAEL, R. D. Boundary value and expansion problems. Amer. Jour. Math.: 43, 69-101, 232-270
(1921) j 44, 129-152 (1922).
CHRIST0PHERS0N, D. G. A new mathematical method for the solution of film lubrication problems. Jour.
Proc. Inst. Mech. Engrs. 146, 126-135 (1942).
CHRISTOPHERSON, D. G. and SOUTHWELL, R. V. Relaxation methods applied to engineering problems. III.
Problems involving two independent variables. Proc. Roy. Soc. Lond. 168A, 317-350 (1938).
C0LLATZ, L. Bemerkungen zur Fehlerabschatzung fur das Differenzenverfahren bei partiellen Different-
ialgleichungen. Zeit. Angew. Math. Mech. 13, 56-57 (1933).
C0LLATZ, L. Das Differenzenverfahren mit hoherer Approximation fur lineare Differentialgleichungen.
Schr. Math, Sem, Inst, Angew, Math, Univ. Berlin 3, 1-34 (1935).
C0LLATZ, L. Uber das Differenzenverfahren bei Anfangswertproblemen partieiier Differential-
gleichungen. Zeit. Angew. Math. Mech. 16, 239-247 (1936).
C0URANT, R. Uber die Methode des Dirichletschen Prinzipes. Math. Ann. 72, 517-550 (1912).
ti
C0URANT, R. Uber die Eigenwerte bei den Differentialgleichungen der mathematischen Physik. Math.
Zeit. 7, 1-57 (1920).
387
BIBLIOGRAPHY
COURANT, R. Uber ein konvergenzerzeugendes Prinzip in der Variationsrechnung. Gott. Nachr. 1922,
COURANT, R. Uber die Theorie der linearen partiellen Differenzengleichungen. Gott .Nachr. 1925,98-109.
COURANT, R. Bemerkungen zur Frage der numerischen Auflosung von Randwertproblemen, die aus der Vari-
ationsrechnung entspringen. Gott. Nachr. 1925, 122-127.
COURANT, R. Uber Randwertaufgaben bei partiellen Differenzengleichungen. Zeit. Angew. Math. Mech.
6, 322-325 (1926).
COURANT, R. Uber direkte Methoden der Variationsrechnung und uber verwandte Fragen. Math. Ann. 97.
711-736 (1927).
COURANT, R. Advanced Methods in Applied Mathematics. New lork, New York Univ. Lectures. 1941.
(mimeo), p. 66-76.
COURANT, R., FRIEDRICHS, K. and LEW, H. Uber die partiellen Differenzengleichungen der mathemati-
schen Pbysik. Math. Ann. 100, 32-74 (1928).
DANIELL, P. J. Orthogonal potentials. Phil. Mag. (7) 2, 247-258 (1926).
DRACH, J. Sur les valeurs moyennes partielles et leur application aux problemes de physique mathe-
matique. C. R. Acad. Sci. Paris 192, 1327-1331 (1931).
DUNCAN, W. J. Galerkin's method in mechanics and differential equations. Gt. Brit. Aeronaut. Research
Comm. Reports and Mem. No. 1798, 33 p. (1937).
DUNCAN, W. J. Principles of Galerkin's method. Gt. Brit. Aeronaut. Research Comm. Reports and Mem.
No. 1848, 24 p. (1938).
DUSINBERRE, G. M. Numerical methods for transient heat-flow. Trans. Amer. Soc. Mech.Eners. 67. 703-
709 (1945).
EMMONS, H. ff. The numerical solution of partial differential equations. Quart. Appl. Math. 2. 173-
195 (1944). .
EMMONS, H. W. The numerical solution of heat-conduction problems. Trans. Amer. Soc. Mech. Eners. 65
607-615 (1943). '
FOWLER, C. M. Analysis of numerical solutions of transient heat-flow problems. Quart. Appl. Math. 3
361-376 (1946). pp **
FOX, L. Solution by relaxation methods of plane potential problems with mixed boundary conditions.
Quart. Appl. Math. 2, 251-257 (1944).
FRANK, P. and VON MISES, R. Die Differential- und Integralgleichungen der Mechanik und Physlk, vol.
1. Braunschweig, Vieweg, 2nd ed. 1930, xxiii + 916 p., p. 734-737.
FRAZER, R. A., JONES, W. P. and SKAN, S. W. Approximations to functions and to the solutions of dif-
ferential equations. Gt. Brit. Aeronaut. Research Comm. Reports and Mem. No. 1799, 33 p.
W/j\) .
FRIEDRICHS, K. 0. and STOKER, J. J. Buckling of the circular plate beyond the critical thrust. Jour.
Appl. Mech. 9, A7-A14 (1942).
FR0CHT, M. M. and LEVEN, M. M. A rational approach to the numerical solution of Laplace's equation.
Jour. Appl. Phys. 12, 596-604 (1941).
GANDY, R. W. G. and SOUTHWELL, R. V. Relaxation methods applied to engineering problems. V. Con-
formal transformation of a region in plane space. Phil. Trans.Roy. Soc. Lond. 238A, 453-475
GERMAY, R. H. Integration, par approximations successives, les equations aux derivees partielles.
C. R. Acad. Sci. Paris 178, 685-488 (1924). «"-"».
388
BIBLIOGRAPHY
GERMAY, R, H, Sur 1* integration par approximations successives des systemes d' equations aux derivees
partielles du premier ordre de forme resolue. G. R. Acad. Sci. Paris 179, 1580-1583 (1924).
GERSCHGORIN, S. Fehlerabschatzung fur das Differenzenverfahren zur Losung partieller Differential-
gleichungen. Zeit. Angew. Math. Mech. 10, 373-382 (1930).
GOLDMANN, E. Anwendung der Ritzschen Method© auf die Theorie der Transversals chwingungen frei
schwingender Platten von rechteckiger, rhombischer, dreieckiger und elliptischer Begrenzung.
(Inaug. -Diss. Breslau.). Breslau, Fleischmann, 1918, 67 p.
GOLDSBOROUGH, G. R. The tides in oceans on a rotating globe. Proc. Roy..Soc. Lond. 117A, 692-718
(1928).
GOLDSBOROUGH, G. R. Note on the method of Ritz for the solution of problems in elasticity* Phil.
Mag. (7) 7, 332-337 (1929).
GRAMMEL, R. Ein neues Verfahren zur Losung technischer Eigenwertprobleme. Ing. Arch. 10, 35-46
(1939) .
HADAMARD, J. Memoire sur le probleme d f analyse relatif a l«equilibre des plaques elastiques in-
castrees. Paris, Mem. Sav. Etrang. (2) 33, «o. 14, 128 p. (1908).
HAUSEN, H. Naherungsverfahren zur Berechnung des Warmeaustausches in Regeneratoren. Zeit. Angew.
Math. Mech. 11, 105-114 (1931).
HENCKY, H. Die Berechnung dunner rechteckiger Platten mit verschwindender Biegungsteifigkeit. Zeit.
Angew. Math. Mech. 1, 81-89, 423-424 (1921).
HENCKY, H. Die numerische Bearbeitung von partiellen Differentialgleichungen in der Technik. Zeit.
Angew. Math. Mech. 2, 58-66 (1922).
HENCKY, H. Eine wichtige Vereinfachung der Methode von Ritz zur angenaherten Behandlung von Vari-
ationsproblemen. Zeit. Angew, Math. Mech. 7, 80-81 (1927).
HUBERT, D. &ber das Dirichletsche Prinzip. Math. Ann. 59, 161-186 (1904) ; Jour. Reine Angew. Math.
tv* io in ttar\c\
HRENKIKOPF, A. Solution of problems of elasticity by the framework method. Jour. Appl. Mech. 8,
A169-A175 (1941).
JAMES, H. M. Some applications of the Rayleigh-Ritz method to the theory of the structure of matter.
Bull. Amer. Math. Soc, 47, 869-884 (1941).
JEFFCOTT, H. K. On the vibration of beams under the action of moving loads, Phil, Mag, (7) 8, 66-97
(1929).
KANTOROVIC, L. Sur une me'thode de resolution &pprochee d' equations differentielles aux derivees
partielles. (Russian and French.). C. R. (Doklady) Acad. Sci. URSS (N.S.) 2, 532-536(1934).
KAISER, R. Rechnerische und experimentelle Ermittlung der Durchbiegungen und Spannungen von quad-
ratischen Platten bei freien Auflagerung an den Randern, gleichmassig verteilter Last und
grossen Ausbiegungen. Zeit. Angew. Math. Mech. 16, 73-98 (1936).
VON KARMAN, T. The engineer grapples with non-linear problems. Bull. Amer. Math. Soc. 46, 615-683
(1940).
KARAS, K. Die Eigenschwingungen inhomogener Saiten. Sitzber. Akad. Wiss. Wien 145 (Ha), 797-816
(1936).
KELLNER, G. W. Die Ionisierungsspannung des Heliums nach der Schrodingerschen Theorie. Zeit. Phys.
44, 91-109 (1927).
KIESSLING, F. Eine Methode zur approximativen Berechnung einseitig eingespannter Druckstabe mit ve-
randerlichen Querschnitt. Zeit. Angew. Math. Mech. 10, 594-599 (1930).
389
BIBLIOGRAPHY
KIMBALL, G. E. and SHORTLEY, G. H. ^ The numerical solution of Schrodinger's equation. Phys. Rev. (2)
KNOTT, C. G. Comparison of Mr. Crawford's measurements of the deflection of a clamped square plate
with Ritz»s solution. Proc. Roy. Soc. Edin. 32, 390-392 (1912).
KOCH, J. J *!f ^T^^f 1 * j^itischer Drehzahlen schnell laufender Wellen.Proc.Intern.Congr.
Appl. Mech. Zurich, 1926. Zurich, Fussli,1927, p. 213-218.
KORMES, M. Numerical solution of the boundary value problem for the potential equation by means of
punched cards. Rev. Sci. Instr. 14, 248-250 (1943).
KORMES, J- J. and KORMES, M. Numerical solution of initial value problems by means of punched-card
machines. Rev. Sci. Instr. 16, 7-9 (1945).
KORN, A. Ueber eine Methode der successive Naherungen zur Losung linearer gewohnlicher und partieller
Dxfferentialgleichungen. Sitzber. Berl. Math. Ges.: 15, 115-119 (1916) j 16, 51-55 (1917).
KOVNER, S. S. On the technique of numerical integration of differential equations with partial
derivatives. C. R. (Doklady) Acad. Sci. URSS (N. S.) 37, 20-23 (1942).
KR0B ' G * M.IS+c iC f Sol f ion °£ ordinary and partial differential equations by means of equivalent
circuits. Jour. Appl. Phys. 16, 172-186 (1945).
KRTLOFF, N.^Sur les generalisations de la methode de Walther Ritz. C. R. Acad. Sci. Paris 164, 853-
KRYLOFF, N. Sur quelques recherches recentes dans le domaine de la solution approche'e des problemes
de la physique mathematique. Atti Congr. Intern. Mat. Bologna 1928, vol. 5. Boloma
Zanichelli, 1931, p. 257-273. '
KRTLOFF, N. and BOGOLIUBOFF, N. On Rayleigh's principle in the theory of differential equations of
mathematical physics and on Euler's method in the calculus of variations. Ann. of Math. (2)
29, 255—275 vl928} .
LAHAYE, E. Sur l'application de la methode des approximations successives a la resolution des equa-
(^^^SnigS)! 101168 lin ^ kireS ** Second ordre - Bun - Acad - R °y- Belg., CI. Sci.
LAPAURI, I. D. On numerical integration of differential equations of hyperbolic type. (Georgian.
Russian summary.). Trav. Inst .Math. Tbilissi (Trudy Tbiliss. Mat. Inst.) 10, 93-109 (1941).
LEMKE, A. Experimentelle Untersuchungen zur W. Ritzschen Theorie der Transversalschwingungen quad-
ratischer Platten. Ann. der Phys. (4) 86, 717-750 (1928).
LEWY, H. &ber einen Ansatz zur numerischen Losung von Randwertproblemen. Gott. Nachr. 1925, 118-121.
""' H ' wfLth^ ^ ^ V ° n Variati0nS - "* Handwertprob-
LIEBMANN, H. Die angenaherte Ermittlung harmonischer Funktionen und konformer Abbildungen (nach
Ideen von Boltzmann und Jacob!) . Sitzber. Akad. ffiss. Munchen 1918, 385-416.
LOVE, A. E. H. The application of the method of W. Ritz to the theory of the tides. Proc. Intern
Congr. Math. Cambridge 1912, vol. 2. Cambridge, Cambridge Univ. Press, 1913, p. 202-208. *
LOCKERT, H. J. Uber die Integration der Differentialgleichungen einer Gleitschicht in zaher Flussig-
keit. Schr. Math. Sem. Inst. Math., Univ. Berlin 1, 245-274 (1933).
MACDONALD,^J. K^L. ^Successive approximations by the Rayleigh-Ritz variation method. Phys. Rev. (2)
MACDONALD, J. K. L. On the modified Ritz variation method. Phys. Rev. (2) 46, 828 (1934).
390
BIBLIOGRAPHY
MACI. G. Sulla integrazione approssimata delle equazioni differential! a derivate parziali. Boll.
Mat. (Firenze) 32, 1-3 (1936).
MAIER, E. Biegeschwingungen von spannungslos verwundenen Staben, insbesondere von Luftschraubenblat-
tern. Ing. Arch. 11, 73-98 (1940).
METER ZUR CAPELLEK, W. Methode zur angenaherten Losung von Eigenwertproblemen mit Anwendungen auf
Schwingungsprobleme. Ann. der Phys. (5) 8, 297-352 (1931).
MIKELADZE, S. E. Uber die numerische Losung der Different ialgleichung kl^ + -|i*±- + l-£ = <f> (x,U,*) .
C. R. (Doklady) Acad. Sci. URSS, (N.S.) 14, 177-179 (1937). ** 2 *9 * x * J
MIKELADZE, S. E. fiber numerische Integration der Laplaceschen und Poissonschen Gleichungen, C. R.
(Doklady) Acad. Sci. URSS, (N.S.) 14, 181-182 (1937).
MIKELADZE, S. E. Uber die numerische Losung der Differentialgleichungen von Laplace und Poisson.
(Russian. German summary.). Bull. Acad. Sci. URSS, Se'r. Math. (Izvestia Akad. Nauk SSSR)
MIKELADZE, S. E. Uber die Losung von Randwertproblemen mit der Differenzenmethode, C. R. (Doklady)
Acad. Sci. URSS,(N.S.) 28, 400=402 (1940).
MIKELADZE, S. E. On the question of numerical integration of partial differential equations by
means of nets. (Russian). Mitt. Georg. Abt. Akad. Wiss. USSR 1, 249-254 (1940).
MIKELADZE, S. E. Numerische Integration der Gleichungen vom elliptischen und parabolischen Typus.
(Russian. German summary.). Bull. Acad. Sci. URSS, Se'r. Math. (Izvestia Akad. Nauk SSSR)
5, 57-74 (1941).
MILNE, W. E. On the numerical solution of a boundary problem.Amer. Math. Month. 38, 14-17 (1931).
MIN0RSKY, N. Control problems. Jour. Franklin Inst. 232, 451-487, 519-551 (1941).
VON MISES, R. and POLLACZEK-GEIRINGER, H. Praktische Verfahren der Gleichungsauf losung. Zeit.
Angew. Math. Mech. 9, 152-164 (1929).
MORGANS W. R. On the solution of second order differential equations satisfying boundary conditions.
Phil. Mag. (7) 32, 483-488 (1941).
MORROW, J. On the lateral vibration of bars of uniform and varying sectional area, Phil. Mag. (6) 10,
113-125 (1905).
MORROW, J. On the lateral vibration of loaded and unloaded bars. Phil. Mag. (6) 11, 354-374 (1906).
MORROW, J. On the lateral vibration of bars subjected to forces in the direction of their axis. Phil.
Mag. (6) 12, 233-243 (1906).
_«.. . ~._ ii i-i 1 J-JM __ii - J -_tl-_„ 4-4__ ** lt.1 n «t.J_J4«a^olll Vox. PV»41 lfnrr ( £.} 13
MU.ttK.UVY, it. UQ l<ne xaoeieix UCLJLOVI/J.UU aim ixuiaviwi \j± uj<»iuj(su-ui4 vx»v» isc**.,* _.».•-*• ». b . N w, — ,
452-465 (1909).
MOSKOVTTZ, D. The numerical solution of Laplace»s and Poisson 1 s equations. Quart. Appl. Math. 2,
148-163 (1944).
NEWING, R. A. On the variation calculation of eigenvalues. Phil. Mag. (7) 24, 114-127 (1937).
HEWING, S. T. Determination of the shearing stresses in axially symmetrical shafts under torsion by
finite difference methods. Phil. Mag. (7) 32, 33-49 (1941).
PANOW, D. Uber die angenaherte numerische Losung des Problems der Warmeleitung. Zeit. Angew, Math.
Mech. 12, 185-188 (1932).
PASCHOUD, M. Application de la methode de Walther Ritz au probleme du regime uniforme dans un tube
a section carree. C. R. Acad. Sci. Paris 159, 158-160 (1914).
391
BIBLIOGRAPHY
PASTERNAK, P. Vereinf achte Berechnung der Biegebeanspruchung in duttnwandigen, kreisrunden Behaltern.
Proc. Intern. Congr. Appl. Mech. Zurich, 1926. Zurich, Fussli, 1927, p. 427-433.
PELLEW, A. and SOUTHWELL, R. V. Relaxation methods applied to engineering problems. VI. The natural
frequencies of systems having restricted freedom. Proc . Roy .Soc. Lond. 175A, 262-290 (1940).
PFEIFFER, F. Zur numerischen Integration hyperbolischer partieller Differentialgleichungen zweiter
Ordnung. Zeit. Angew. Math. Mech. 18, 233-236 (1938).
PHILLIPS, H. B. and WIENER, N. Nets and the Dirichlet problem. Jour. Math. Phys. (M.I.T.)2, 105-124
(1923). '
P1CARD, E. Memoire sur la thebrie des equations aux derivees partielles et la methode des approxi-
mations successives. Jour. Math. Pures Appl. (4) 6, 145-210, 231 (1890).
PLANCHEREL, M. Sur la methode d'integration de Ritz. Bull. Sci. Math. (2)i 47, 376-383, 397-412
(1923) J 48, 12-48, 58-80, 93-109 (1924).
POLHAUSEN, B. E. Berechnung der Eigenschwingungen statisch bestimmter Fachwerke. Zeit. Angew. Math.
Mech. 1, 28-42 (1921).
PRASAD, G. The numerical solution of partial differential equations. Phil. Mag. (7) 9, 1074-1081
(1930).
LORD RAYLEIGH. On the calculation of the frequency of vibration of a system in its gravest mode with
an example from hydrodynamics. Phil. Mag. (5) 47, 566-572 (1899).
LORD RAYLEIGH. On the calculation of Chladni's figures for a square plate. Phil. Mae. (6) 22. 225-
229 (1911). 6 ' '
RICHARDSON, L. F. The approximate arithmetical solution by finite differences of physical problems
involving differential equations with an application to the stresses in a masonry dam.Phil.
Trans. Roy. Soc. Lond. 210A, 307-357 (1910).
RICHARDSON, L. F. How to solve differential equations approximately by arithmetic. Math.Gaz. 12.415-
421 (1925).
RICHARDSON, R. G. D. A new method in boundary problems from differential equations. Trans .Amer. Math.
Soc. 18, 489-518 (1917).
RITZ, W. Uber eine neue Methode zur Losung gewisser Variationsprobleme der mathematischen Physik.
Jour.Reine Angew. Math. 135, 1-61 (1908), or Gesammelte Werke,Paris, Gauthier-Villars.1911.
p. 192-250. '
RITZ, W. Uber eine neue Methode zur Losung gewisser Randwertaufgaben. Gott. Nachr. 1908, p. 236-248.
or Ges. Werke, 1911, p. 251-264.
RITZ, W. Theorie der Transversalschwingungen einer quadratischen Platte mit freien Randern. Ann.
der Phys. (4) 28, 737-786 (1909), or Ges. Werke, 1911, p. 265-316.
ROSENBLATT, A. Sur l'application de la methode des approximations successives de M. Picard a 1' etude
de certaines equations non lineaires du quatrieme ordre. Bull. Sci. Math. (2) 58, 117-136
151-168 (1934).
ROSENBLATT, A. Sur les equations biharmoniques non lineaires a deux variables independantes.Bull.
Sci. Math. (2) 58, 248-264 (1934).
LE ROOX, J. Sur le probleme de Dirichlet. Jour. Math. Pures Appl. (6) 10, 189-230 (1914).
RUNGE, C. and W3XLERS, F. A. Numerische und graphische Quadratur und Integration gewohnlicher und
partieller Differentialgleichungen. Ency. Math. Wiss. Leipzig, Teubner, 1915, vol. 11(3) 2
article H C2, p. 47-176. *
SHERWOOD, T. K. and REED, C. E. Applied Mathematics in Chemical Engineering. New York, McGraw-Hill.
1938, xi + 403 p., p. 241-255. *
392
BIBLIOGRAPHY
-._ ^ - — — -"■» — m t „ _..___.* ,«1 »-T «>*•?-»»> «■? TonloAili; apiin-Hftn,. Jour. AddI* PhyS. 9*
SHORTLEI, G. H. ana HBWiut, n. ihe nusaeixCoj. •«*«»*»!! «- ~ap»s s * sl *- v
SHORTLEI, G. H. and WELLER, R. Calculation of stresses within the boundary of photoelastic models.
Jour. Appl. Mech. 61, A71-A78 (1939).
SHORTLEI, G. H„ KELLER, R. and FRIED, B. Numerical solution of Laplace's and ^ Poiss ^ «*»%£»
with applications to photoelasticity and torsion. Ohio State Univ. Studies, Engrg. Series,
vol. 11, No. 5. Engrg. Exp. Station, Bull. No. 107. Columbus, Ohio, 1940, iii + 51 P.
SIDDIQI, M. R. Boundary Problems in Non-linear Partial Differential Equations. Lucknow Univ. Studies,
No. 11. Allahabad, India, Allahabad Lair Journal Press, 1939, xiv + 136 p.
S0K0LNIK0FF, I. S. On a solution of Laplace's equation with an application to the torsion problem
for a polygon with reentrant angles. Trans. Amer. Math. Soc. 33, 719-73^ KrjjX).
SOUTHWELL, R. V. Relaxation Methods in Engineering Science. A Treatise on Approximate Computation.
"Oxford Engrg. Sci. Ser., New York, Oxford Univ. Press, 1940, vii + *?* p., euap. ..«., .*~.
SOUTHWELL, R. V. New pathways in aeronautical theory. Fifth Wright Brothers Lecture. Jour. Aeronaut.
Sci. 9, 77-89 (1942).
SOUTHWELL, R. V. and VAISEY, G. Relaxation methods applied to engineering problems. VIII. Plane-
potential problems involving specified normal gradients. Proc. Roy. Soc. Lond. l«<dA, i^i-
151 (1943).
TAMARKIN, J. D. and FELLER, W. Partial Differential Equations. (Mimeo.) Providence, Brown Univ.,
1941, chap. V, p. 160-196.
TEMPLE, G. The general theory of relaxation methods applied to linear systems. Proc. Roy. Soc. Lond.
1£9A, 476-500 (1939).
TH0M, A. The flow past circular cylinders at low speeds. Proc. Roy. Soc. Lond. 14L4, 651-669 (1933).
TH0RNE, C. J. and ATANASOFF, J. V. A functional method for the solution of thin plate problems ap-
" ' -. . . - j _i-jl- _**>- _*.-..,l ~k4«+ l«orf Tnrn State P.nll - .Tnur- Scl.lZi...
plied to a square, cxaunpeu pxeiuc: mwi » ^^v* cm. ^.m- -— . - — - ■,
333-343 (1940).
TIM0SHENK0, S. A membrane analogy to flexure. Proc. Lond. Math. Soc. (2) 20, 398-407 (1921;.
TIM0SHENK0, S. The approximate solution of two-dimensional problems in elasticity. Phil.Mag. (6) 47,
1095-1104 (1924).
T3MDSHENK0, S. Theory of Plates and Shells. New York, McGraw-Hill, 1940, xii + 492 p., p. 180-187.
TREFFTZ, E. Ein Gegenstuck zum Ritz'schen Verfahren. Proc. Intern. Congr. Appl. Mech. Zurich, 1926.
Zurich, Fussli, 1927, p. 131-137.
T5EFFT7- E. Konvereenz und Fehlerabschatzung beim Ritzschen Verfahren. Math. Ann. 100, 503-521
(1928).
TREFFTZ, E. fiber Fehlerabschatzung bei Berechnung von Eigenwerten. Math. Ann. 108, 595-604 (1933) .
TREFFTZ, E. Die Bestimmung der Knicklast gedruckter, rechteckiger Platten. Zeit. Angew. Math. Mech.
15, 339-344 (1935).
VASILESC0, F. Sur une methbde de M. Riabouchinsky ayant pour but de resoudre le probleme de Dirich-
let, en vue du calcul du potentiel des vitesses. C. R. Acad. Sci. Paris 193, 1162-1164
(1931).
VAZS0NYI, A. A numerical method in the theory of vibrating bodies. Jour. Appl. Phys. 15, 598-606
(1944).
393
BIBLIOGRAPHY
VERNOTTE, P. Meihode tres geherale pour e"tudier le debut des perturbations regies par les equations
aux derivees partielles de la physique mathematique. Application a la chaleur et 'a l'hydro-
dynamique. C. R. Acad. Sci. Paris 210, 42-44 (1940).
VOIGT, W. Die Grundschwingungen kreisformiger Klangplatten aus Kristallen. Gott.Nachr. 1915,345-391.
WASCHAKIDZE, D. Uber die numerische Losung der biharmonischen Gleichung. (Russian. German sum-
mary.). Trav. Inst. Math. Tbilissi (Trudy Tbiliss. Mat. Inst.) 9, 61-73 (1941).
WEINSTEIN, D. H. Modified Ritz method. Proc. Nat. Acad. Sci. U.S.A. 20, 529-532 (1934).
WEINSTEIN, A. On a minimal problem in the theory of elasticity. Jour. Lond. Math. Soc. 10, 184-192
(1935).
WEINSTEIN, A. Les vibrations et le calcul des variations. Portugaliae Math. 2, 36-55 (1941).
WELLER, R., SHORTLEY, G. H. and FRIED, B. The solution of torsion problems by numerical integration
of Poisson's equation. Jour. Appl. Phys. 11, 283-290 (1940).
WOLF, F. Uber die angenaherte numerische Berechnung harmonischer und biharaonischer Funktionen.
Zeit. Angew. Math. Mech. 6, 118-150 (1926).
23. INTEGRAL EQUATIONS
BAIRSTOW, L. and BERRY, A. Two dimensional solutions of Poisson's and Laplace's equations. Proc.
Roy. Soc. Lond. 95A, 457-475 (1919).
BATEMAN, H. Report on the history and present state of the theory of integral equations. British
Assoc. Rep. 1910, p. 345-424.
BATEMAN, H. On the numerical solution of linear integral equations. Proc. Roy. Soc. Lond. 100A, 441-
448 (1922).
ii
BLOCK, H. Sur la solution de certaines equations fonctionnelles. Arkiv for Mat. 3, No. 22,18 p.,
(1907).
BLUMENTHAL, 0. Uber die Knickung eines Balkens durch Langskrafte. Zeit. Angew. Math. Mech. 17, 232-
244 (1937).
BOCHER, M. An Introduction to the Study of Integral Equations. Cambridge Math. Tracts No. 10,
London, Cambridge Univ. Press, 2nd ed. 1914, reprint 1926, 70 p., p. 13-19, 24-37.
BOGGXD, T. Integrazione dell'equazione funzionale che regge la caduta di una sfera in un liquido
viscoso. Rend. Accad. dei Lincei Roma (5) 16-2, 613-620, 730-737 (1907).
COLLATZ, L. „ Vergleich der Integralgleichungsmethode von Bucerius mit dem Ritzschen Verfahren zur
genaherten Losung von Differentialgleichungen. Astr. Nachr. 271, 116-120 (1941).
COLLET, A. Sur les solutions approchees de certaines equations integrales non lineaires. Ann.Toulouse
(3) 4, 199-249 (1912).
CROUT, P. D. An application of polynomial approximation to the solution of integral equations
arising in physical problems. Jour. Math. Phys. (M.I.T.) 19, 34-92 (1940).
DAVIS, H. T. A Survey of Methods for the Inversion of Integrals of the Volterra Type. Indiana Univ.
Studies, 14, No. 76-77, 72 p. (1927).
VAN DEN DUNGEN, F. H. Les equations integrales "a plusieurs parametres et la technique des vibrations.
Proc. Intern. Congr. Appl. Mech. Zurich 1926. Zurich, Fussli, 1927, p. 113-118.
ENSKOG, D. Kinetische Theorie der Vargange in massig verdunnten Gasen. (Diss. Uppsala). Uppsala,
Almquist and Wiksells, 160 p., 1917.
394
BIBLIOGRAPHY
ENSKOG, D* Die numerisc-he Bereehnung der Vorgange in raassig verdunnten Gasen. Arkiv for Mat. 16,
""""""* "" No. 16* 60 p.. 1921.
ENSKOG, D. Eine allgemeine Methode zur Auflosung von linearen Integralgleichungen. Math. Zeit. 24,
670-685 (1926).
FRANK, P. and VON MISES, R. Die Differential- und Integralgleichungen der Mechanik und Physlk,vol.
1. Braunschweig, Vieweg, 2nd ed. 1930, p. 555-562.
FREDHOLM, I. Sur une nouvelle methode pour J.a resolution du probleme de Dirichlet. Ofversigt af
Kongl. Svenska Vetenskaps Akademiens Forhandlingar 57, 39-46 (1900).
FREDHOLM, I. Sur une classe d'equations fonctionnelles. C. R. Acad. Sci. Paris 134, 1561-1564 (1902).
FREDHOLM, I. Sur une classe de transformations rationnelles. C. R. Acad. Sci. Paris 134, 219-222
(1902).
„ T , TO „„. r „ , „ _, A%J z — 4.4 — « c«^t4^.noc A^ta «»+*»- on . ?A«;-^00 doo^.
GORGIDZE, A. I. and RUCHADZE, A. K. On a numerical solution of integral equations of the plane
problem of the theory of elasticity. (Russian.). Mitt. Georg. Abt. Akad, ifisa. USSR 1, 255-
OCfS (*t Or C\\
GTLLENBERG, W. fiber eine graphische Losung einer Integralgleichung. Astr. Nachr. 269, 52-53 (1939).
HAVELOCK, T. H. The solution of an integral equation occurring in "certain problems of viscous fluid
motion. Phil. Mag. (6) 42, 620-628 (1921).
HEGKE, E. Uber die Integralgleichung der Kinetischen Gastheorie e Math- Zeit, 12, 274-286 (1922).
HELLINGER, E. and TOEPLITZ, 0. Integralgleichungen und Gleichungen mit unendlichvielen Unbekanntea
Ency. Math. Diss. vol. 2 (3), article II C13, 1335-1597 (1927).
HUBERT, D. Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen. Gott. Nachr. 1904,
49-91, 213-259.
HILDEBRAND, F. B. The approximate solution of singular integral equations arising in engineering
practice. Proc. Amer. Acad. Arts Sci. 74, 287-295 (1941).
HILDEBRAND, F. B. and CROUT, P. D. A least square procedure for solving integral equations by
polynomial approximation. Jour. Math. Phys. (M.I.T.) 20, 310-335 (1941).
HILL, G. W. On the part of the motion of the lunar perigee which is a function of the mean motions
of the sun and moon s Acta* Math* 8, 1-36 (1886),
HITCHOCK, F. L. A method for the numerical solution of integral equations. Jour. Math. Phys.
(M.I.T.) 1, 88-104 (1922).
HORT, Yh Die Differentialgleichungen des Ingenieurs. Berlin, Springer, 2nd ed. 1925, xii + 700 p.,
p. 639-667.
HOWLAND, R. C. J. Application of an integral equation to the whirling speeds of shafts. Phil. Mag.
(7) 3, 513-528 (1927).
INGRAM, W. H. On the integral equations of continuous dynamical systems. Phil. Mag. (7) 30, 16-38
(1940).
K3ESSLING, F. Eine Methode zur Approodmativen Berechnung einseitig eingespanneter Druckstabe mit
veranderlichem Querschnitt. Zeit. Angew. Math. Mech. 10, 594-599 (1930).
KNOTT C. G. The propagation of earthquake waves through the earth and connected problems, Proc*
Roy. Soc. Edin. 39, 157-208 (1919).
vrwim lr ikon ©■*»! nsuss Verfahren zur Erssittlup" von Schi?ir ,<T ur ,£r s r >erioden von Turbinenscheibens
* pp^ Interm congr. Appl. Mech. Zurich 1926. Zurich, Fussli^ 1927, p. 173-177.
395
BIBLIOGRAPHY
KORN, A. Uber freie und erzwungene Schwingungen. Leipzig, Teubner, 1910, v + 136 p., p. 50-136.
KORH, A. Uber die Anwendung der Methode der sukzessiven Naherungen zur Losung von linearen Inte-
gralgleichungen mit unsymmetrischen Kernen. Arch. Math. Phys. (3): 25, 148-173 (1917) J
27, 97-120 (1918).
KOSTITZIN, V. A. Applications des equations integrales. (Applications statistiques). Mem. Sci.Math.
fasc. 69, 48 p. (1935).
MAGNUSSON, P. C. A numerical method of solving integral equations in two independent variables.
Jour. Math. Phys. (M.I.T.) 21, 250-263 (1942).
MEYER ZUR CAPELLEN, W. Kleine Anderungen des Kerns einer symmetrischen homogenen, linearen Inte-
gralgleichung. Zeit. Angew. Math. Mech. 13, 323-324 (1933).
MICHE, R. Le calcul pratique de problemes elastiques a deux dimensions par la methode des equations
integrales. Proc. Intern. Congr. Appl. Mech. Zurich 1926. Zurich, Fiissli, 1927, 126-130.
MIKELADZE, S. E. De la re'solution numerique des equations integrales. (Russian. French summary.).
Bull. Acad. Sci. URSS (Izvestia Akad. Nauk SSSR) (7) 1, 255-300 (1935).
MUNTZ, C. Solution directe de 1' equation se'culaire et de quelques problemes analogues transcendantes.
C. R. Acad. Sci. Paris I56, 43-46 (1913).
NYSTROM, E. J. Uber die praktische Auflosung von linearen gleichungen mit Anwendungen auf Rand-
wertaufgaben der Potentialtheorie. Soc. Sci. Fennica Comment, Phys. -Math. 4, No. 15,
-52 p. (1928).
NYSTROM, E. J. Uber die praktische Auflosung von Integralgleichungen. Soc. Sci. Fennica Comment.
Phys.-Math. 5, No. 5, 22 p. (1929).
NYSTROM, E. J, Uber die praktische Auflosung von Integralgleichungen mit Anwendungen auf Rand-
wertaufgaben. Acta Math. 54, 185-204 (1930).
OBERG, E. N. The approximate solutions of integral equations (abstract). Bull. Amer. Math. Soc .39*
513 (1933).
PEKERIS, C. L. A pathological case in the numerical solution of integral equations. Proc. Nat.
Acad. Sci. U.S.A. 26, 433-437 (1940).
PICARD, E. Sur une equation fonctionnelle. C. R. Acad. Sci. Paris 139, 245-248 (1904).
PRAGER, W. Die Druckverteilung an Korpern in ebener Potentialstromung. Phys. Zeit. 29, 865-869
(1928).
PRASAD, G. On the numerical solution of integral equations. Proc.Edin. Math. Soc. 42, 46-59 (1924).
PRASAD, G. On the numerical solution of integral equations. Proc. Intern. Congr .Math, Toronto
1924, vol. 1. Toronto, Univ. of Toronto Press, 1928, p. 683,
REIZ, A. On the numerical solution of certain types of integral equations. Arkiv for Mat, 29 A,
Ho. 29, 21 p. (1943).
SCHMIDT, E. Zur Theorie der linearen und nichtlinearen Integralgleichungen. Math . Ann. : 63, 433-
476 (1907) j 64, 161-174 (1907).
SCHROEDER, K. Uber die Prandtlsche Integro-Differentialgleichung der Tragflugeltheorie. Abh. Preuss.
Akad. Wiss. Math.-Nat. Kl. 1939, No. 16, 35 p.
SCHWERIN, E. Uber die Transversalschwingungen von Staben veranderlichen Querschnitts. Proc.
Intern. Congr. Appl. Mech. Zurich 1926. Zurich, Fiissli, 1927, p. 138-145.
SERINI, R, Teoria del condensatore electrico a piatti circolari. Rend. Accad. dei Lincei Roma
(5) 29-2, 34-37, 257-261 (1920).
396
BIBLIOGRAPHY
TEOFILATO, P. Risoluzione grafica e nuraerica approssimata di un equazione integrale. Atti della
"Pontificia Accad. Romana dei Nuovi Lincei 76, 36-45 (1922-1923) .
TRICOMI, F. Sulla risoluzione numerica delle equazioni integrali di Fredholm. Rend. Accad. dei
Lincei Roma (5) 33-1, 483-486 (1924).
TRICOMI, F. Ancora sulla risoluzione numerica delle equazioni integrali di Fredholm. Rend. Accad.
dei Lincei Roma (5) 33-2, 26-30 (1924).
VTTERBI, A. Sulla risoluzione approssimata delle equazioni integrali di Volterra e sulla appli-
cazione di questa alio studio analitico delle curve. Rend. 1st. Lombardo (2) 45, 1027-1060
(1912).
NHITTAKER, E. T. On the numerical solution of integral-equations, Proc. Roy, Soc. Lond. 94A,367-
383 (1918).
WHITTAKER, E. T. and ROBINSON, G. The Calculus of Observations. Glasgow, Blackie, 3rd ed. 1942,
WIARDA, G. Integralgleichungen, unter besondere Berucksichtigung der Anwendungen. Leipzig, Teubner,
Samniiung Math.-phys. Lehrbucher, 1930, 183 p.
397
ABBREVIATIONS
Abh. Akad. Munchen: Abhandlungen der Gesellschaft Bayerischen Akademie der Wissenschaften. Math-
ematisch-naturwissenschaftliche Abteilung.
Abh. Ges. Wiss. Leipzig: Abhandlungen der mathematisch-physischen Klasse der Sachsischen Akademie
der Wissenschaften.
Acad. Roum. Bull. Sect. Sci.: Academie Romnaine Bulletin de la section scientifique. Bucharest.
Acad. Roy. Belgique CI. Sci. Mem Coll.: Academie Royale de Belgique. Classe des Sciences. Memoires
collections en 4° et 8°.
Acad Sci. RSS Ukraine Rec. Trav. (Zbirnik Prace) Inst. Math.: Academie des Sciences de l'Ukraine.
Institut mathematique, Reeuillis Travaux. (Akademiia Nauk URSR. Institut Matematiki Zbir-
nik Prace).
Acta Math.: Acta Mathematica. Uppsala.
Acta Soc. Sci. Fennicae: Acta Societatis Scientiarum Fennicae. A: Opera Physico-mathematica. Hel-
singfors (Helsinki).
Acta Univ. Szeged Sect. Sci. Math: Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae
Francisco-Iosephinae. Sectio Scientiarum Mathematicarum. Szeged.
Aircraft Engrg.: Aircraft Engineering. London.
Amer. Jour. Math.: American Journal of Mathematics. Baltimore.
Amer. Math. Month: The American Mathematical Monthly. The Official Journal of the Mathematical
Association of America.
Ann. de Gergonne: Annales de Mathematiques Pures et Applique'es. Recueil Periodique, Redige' et Pub-
lie'e par J. D. Gergonne.
Ann. de l'Observ.: Annales de l'Observatoire de Paris.
Ann. de Phys. : Annales de Physique. Paris.
Ann. der Phys. : Annalen der Physik. Leipzig.
Ann. Ecole Norm. Sup.: Annales Scientifiques de l'Ecole Normale Superieure. Paris.
Ann. Harvard Coll. Obs. Annals of the Astronomical Observatory of Harvard College.
Ann. Math. Statist.: The Annals of Mathematical Statistics. The Official Journal of the Institute
of Mathematical Statistics. Baltimore.
Ann. Mat. Pura Appl.: Annali di Matematica Pura ed Applicata. Bologna.
Ann. of Math.: Annals of Mathematics. Princeton.
Ann. Sci. Univ. Jassy: Annales Scientifiques de l'Universite' de Jassy.
Ann. Toulouse:^ Annales de la Faculte' des Sciences de l'Uhlversite'de Toulouse pour les Sciences
Mathematiques et les Sciences Physiques.
An. Soc. Sci. Argentina: Anales de la Sociedad Cientifica Argentina, Adoptados para sus Publicac-
lones por la Academia Nacional de Ciencias Exactas, Fisicas y Naturales. Buenos Aires.
Appl. Math. Mech. (Akad. Nauk SSSR Prikl. Mat. Mech.): Applied Mathematics and Mechanics (Priklad-
naia Matematika i Mekhanika).
Arch. Math. Phys.: Archiv der Mathematik und Physik mit besonderer Rucksicht auf die Bedurfnisse
der Lehrer an hoheren Unterrichtaanstalten. Gegrundet 18U durch J. A. Grunert.
Arch. Sci. Phys. Nat. Geneve: Bibliotheque Universelle. Archives des Sciences Physiques et Nature-
lies. Geneva.
398
ABBREVIATIONS
j^jciv fl T |»a+ #: Arkiv for Matematik astronomi och fysik s Utgivet av K* Svenska Vetenskapsakademien.
Stockholm*
Astr. Jour.: Astrophysical Journal. An International Review of Spectroscopy and Astronomical Phys-
ics. University of Chicago Press.
Astr. Jour. Soviet Union: Astronomical Journal of the Soviet Union (Akademiia Nauk SSSR. Astronom-
iceskii Zhurnal.). Moscow.
Astr. Nachr.: Astronomische Nachrichten. Kiel.
Atti Accad. Sci. Torino: Atti della Reale Accademia della Scienze di Torino. I: Classe di Scienze,
Fisiche, Matenatiche e natural! ,
Beitrage zur Geophys.: Beitrage zur angewandten Geophysik. (Started as Gerlands Beitrage zur Geo-
physik). Leipzig,
Beitr. Physik frei. Atmosph.: Beitrage zur Fhysik der freien Atmosphare. Zeitsehrift fur !i«»-
forschung der hoheren Luftschichten und der Stromungserscheinungen in der Atmosphare.
Leipzig.
«— tr v c~~u„, *v*^ is-*— *~» Ta4»»4 M « T!a«4«vi*-ffi JtKar. .-«« T?a^Viancii!in£rer. d«r S&ehsisehen Akademie
der Wissenschaften zu Leipzig. Mathematisch-physische Klasse.
Boll. Mat.: II Bolletino di Matematiea. Giornale Scientifico-didattico per l'Incremento degli Studi
Matematici nelle Scuole Medie... Florence.
Boll. Un. Mat. Ital.: Bolletino della Unione Matematica Italiana. Bologna.
Brit. Assoc. Rep.: British Association for the Advancement of Science. Report of the Annual Meet-
ing. London.
Bull. Acad, Sci. URSS Ser. Math. (Izvestia Akad. Nauk SSSR): Bulletin de I'Aeademie des Sciences
de l'URSS. Classe des Sciences mathematiques et naturelles.
Bull* Internal* Acad= Sci* Gracovia. CI, Sci. Math. Nat~: Bulletin International de I'Aeademie des
Sciences de Cracovie. Classe des Sciences Mathematiques et Naturelles. Polaka Akademja
Umiejetnosci. Cracow.
Bull. Intern. Acad. Polon. Sci. Lett., CI. Sci. Math. Nat.: Bulletin International de l'Academie
Polonaise des Sciences et des Lettres, Classes des Science Mathematiques et Naturelles.
Serie A: Sciences Mathematiques. Polska Akademja Umiejetnosci. Cracow.
Bull. Aser. Math. Sec: Bulletin of the American Mathematical Society,
Bull. Calcutta Math. Soc: Bulletin of the Calcutta Mathematical Society.
_ __ _. _ . _. »r .. »>.>n. T^-i-i _j-j _ j_ ■«_ m j e_j ___ m.__ J —. _ ». _4- \t~i.l~*iL.~t.i~..~.~
[-mil. CI. SCI.— myS. HaaWl. RieXX: DIUJLeuXU UB MX vxoaoo noo w>«aci*>oo i lyo^uoo <cu «awiaun,J4uoo.
(Ukrainska Akademiia Nauk. Zapiski Fizicno-matematicnogo Viddilu.), Kiev.
Bull. Math. Phys, Ecole Polyt. Bucharest: Bulletin de Mathematiques et de Physiques Pures et Ap-
pliquees de 1* Ecole Polytechnique Roi Carol II, Bucarest.
Bull. Nat. Res. Council: Bulletin of the National Research Council. Washington, D. C.
Bull. Sci. Ec. Timisoara: Bulletin Scientifique de l'Ecole Polytechnique de Timisoara. Timisoara,
Roumania.
Bull. Sci. Math.: Bulletin des Sciences Mathematiques. (Started as Bulletin des Sciences Mathemat-
iques et Astronomiques.). Paris.
Bull. Soc. Math. France: Bulletin de la SocLete" Mathematique de France Public par les Secretaires,
Paris.
399
ABBREVIATIONS
Bull. Soc. Sci. Gluj: Bulletin de la Societe des Sciences de Cluj. (Buletinul Societa^ii de §tinte
din Cluj.).
Bull. Univ. Tashkent: Bulletin de l'Universite'de l'Asie Centrale. (Biulletini Sredne-Aziatskogo
Gosudarstvennogo Universiteta.). Tashkent.
Casopis pest. mat. a fys.: Casopis pro Pestovani Matematiky a Fysiky v Praze. Prague.
Comment . Acad. Sci. Petropol.: Commentarii Academiae Scientiarum Imperialis Petropolitanae.
Comment. Math. Helv.: Commentarii Matheraatici Helvetic!. Editi Societate Mathematica Helvetica.
Zurich.
C. R. Acad. Sci. Paris: Comptes Rendus Hebdomaires des Seances de l'Academie des Sciences par lilt.
les Secretaires Perpetuels. Paris.
Danske 7id. Selsk. Math. -Fys. Medd.: Det Kgl. Danske Videnskabernes Selskab. Matematisk-fysiske
Meddelser. Copenhagen.
Deutsche Math.: Deutsche Mathematik. Im Auftrage der Deutschen Forschungsgemeinschaft.
Duke Math. Jour.: Duke Mathematical Journal. Durham, N. C.
Edin. Math. Tracts: Edinburgh Mathematical Tracts.
Electrotech. Zeit.: Elektrotechnische Zeitschrift. Organ des Elektrotechnischen Vereins seit 1880
und des Verbandes Deutscher Elektrotechniker seit 18%.
L'Ens. Math.: L'Enseignement Mathematique. Organ Officiel de la Commission Internationale de l'En-
seignement Mathematique. Paris and Geneva.
Ergebnisse der Math.: Ergebnisse der Mathematik und ihrer Grenzgebiete. Berlin.
Gaz. Mat.: Gazeta l!atematica Apare Odata- pe Luna. Bucharest.
Gott. Nachr.: ffechrichten von der Gessellschaft der V/issenschaften zu Gottingen. Mathematisch-Physi-
kalische Klasse.
Greenwich Observations: Observations made at the Royal Observatory, Greenwich in the year , in
Astronomy, Magnetism, and Meteorology.
Indian Jour. Phys.: Indian Journal of Physics and Proceedings of the Indian Association for the
Cultivation of Science.
Ing.-Arch.: Ingenieur-Archiv. Berlin.
Jap. Jour. Math.: Japanese Journal of Mathematics. Tokyo.
Jber. Deutsch. Math. Verein.: Jahresbericht der Deutschen Mathematiker-Vereinigung. Leipzig.
Jour. Aeronaut. Sci.: Journal of the Aeronautical Sciences. Easton,, Perm.
Jour. Amer. Statist. Assoc: Journal of the American Statistical Association. Washington, D. C.
Jour. Appl. Mech.: Journal of Applied Mechanics. Publ. as Supplement to Trans. Amer. Soc.Mech.Engrs.
Jour. Appl. Phys.: Journal of Applied Physics. American Institute of Physics. New York.
Jour. Brit. Astr. Assoc: Journal of the British Astronomical Association.
Jour. Exp. Teor. Phys.: Zhurnal Eksperimental'noi i Teoreticeskoi Fisiki. Akademiia Nauk SSSR Len-
ingrad.
Jour. Ecole Polytech. Paris: Journal de l'Ecole Polytechnique Publie par le Conseil d'Instruction de
cet Etablissement . Paris.
400
ABBREVIATIONS
Jour. Franklin Inst,: Journal of the Franklin Institute devoted to Science and the Mechanic Arts,
Philadelphia.
Jour, Inst, Actuar,: Journal of the Institue of Actuaries, London,
Jour. Lond. Math. Soc: The Journal of the London Mathematical Society,
Jour. Math, Phys. (M.I.T.): Journal of Mathematics and Physics, Massachusetts Institute of Technol-
ogy.
Jour. Math. Pures Appl.: Journal de Mathematiques Pures et Appliquees. Paris.
Jour. Mysore Univ. Sect. B: The Half-yearly Journal of the Mysore University. New Series. Section B-
Science.
Jour. Opt. Soc. Amer.: Journal of the Optical Society of America. American Institute of Physics. New
York.
Jour. Reine. Angew. Math.: Journal fur die Reine und Angewandte Mathematik. Berlin.
Jour- Roy. Aeronaut. Soc: The Journal of the Royal Aeronautical Society with which is incorporated
The Institution of Aeronautical Engineers. A Monthly Illustrated Magazine Devoted to All
Subjects Connected with the Navigation of Air. London.
Jour. Sci. Instr.: Journal of Scientific Instruments. A Publication Dealing with their Principles,
Construction and Use and the Applications of Physics in Industry. Produced by the Institute
of Physics with the Cooperation of the National Physical Laboratory. Cambridge, Eng.
Lunds Univ. Arsskrift: Acta Universitatis Lundensis. Nova Series. Lunds Universitets Arsskrift. Ny
Foljd. Andra Avdelningen. Medicin Samt Matematiska och naturvetenskapliga Amnen.
Mass. Inst, of Tech. Pubis. (Math.): Publications from the Massachusetts Institute of Technology.
Contribution from the Deparfcuenb of Mathematics.
Math. Ann.: Mathematische Annalen. Berlin.
Mathematica (cluj): Mathematica, Publicatie a Seminarului de Matematici al universitatii, Cluj.
Math. Gaz.: The Mathematical Gazette. London.
Math. Mag.: The Mathematical Magazine. A Journal of Elementary Mathematics. Washington, D. C.
Math. Naturwiss. Anz. Ungar. Akad. Wiss.: Mathematischer und naturwissenschaftlicher Anzeiger der
Ungarischen Akademie der Wissenschaften. Budapest.
Math. Notae; Mathematicae Notae. Boletin del Instituto de Matematica, Universidad Nacional del Lito-
ral. Facultad de Ciencias Matematicas. Rosario, Argentina.
Math. Repository: New Series of the Mathematical Repository. By Thomas Leybourn of the Royal Mili-
tary College. London.
Math. Student: The Mathematics Student. A Quarterly Dedicated to the Service of Students and Teachers
in India. Published by the Indian Mathematical Society. Madras.
Math. Visitor: The Mathematical Visitor. Erie, Penn.
Math. Zeit,: Mathematische Zeitschrift, Berlin,
Mat. Tidsskr. B: Matematisk Tidsskrift B, Udgivet af Matematisk Forening i K^benhavn.
Mem. Acad. Roy. Bruxelles: Memoires de 1' Academe ImpeViale et Royale des Sciences et Belles-Lettres
de Bruxelles.
Mem. Acad. St. Petersbourg: Memoires de l'Academie Imperiale des Sciences de St. Petersbourg. (Za-
piski Imperatorskoi Akademii Nauk.).
Mem. Coll. Sci. Kyoto Imperial Univ.: Memoirs of the College of Science, Kyoto Imperial University.
Series A.
401
ABBREVIATIONS
Mon. Acad. Sci, Kiev: Acadelnie des Sciences d' Ukraine Memoires de la Classe des Sciences Mathemati-
ques et Physiques (Trudy Fizichno-Mathematichnii Viddil) or Memoires de la classe des Sci-
ences Naturelles et Techniques (Trudy Prirodnichno-Tekhnichnii Viddil) .
Mem. Roy, Met. Soc.: Memoirs of the Royal Meteorological Society. London.
Memorie Reale Accad. d'ltalia: Reale Accademia d'ltalia. Memorie della Classe di Scienze Fisiche,
Matematiche, e Natural!. Rome.
Mem. Sci. Math.: Memorial des Sciences Mathematiques. Paris.
Mem. Soc. Royale Sci. Liege: Memoires de la Societe Royale des Sciences de LiSge.
Mess, of Math.: The Messenger of Mathematics. Cambridge.
Meteorol. Zeit.: Meteorologische Zeitschrift. Im Auftrage der Deutschen Meteorologischen Gesells-
chaft, Munchen.
Mitt. Georg. Abt. Akad. Wiss.: Akademiia Nauk SSSR (Leningrad). Mitteilungen der Georgischen Abtei-
lung der Akademie der Wissenschaften der USSR. (Gruzinskii Filial. Soobsceniia...).
Mitt. Math. Ges. Hamburg: Mitteilungen der Mathenatischen Gesellschaft in Hamburg.
Mitt. Verein. Schweiz. Versich. Math.: Mitteilungen der Vereinigung Schweizerischer Versicherungs-
mathematiker. (Bulletin de 1* Association des Actuaires Suisses.). Bern.
Monatsh. Math. Phys.: Monatshefte fur Mathematik und Physik.
Month. Not. Roy. Astr. Soc: Monthly Notices of the Royal Astronomical Society, Containing Papers,
Abstracts of Papers and Reports of the Proceedings of the Society. London.
Month. Weather Rev.: Monthly Weather Review. U. S. Weather Bureau. Washington, D. C.
Nat. Math. Mag.: National Mathematics Magazine. (Formerly Mathematics News Letters.). Baton Rouge,
La.
Nouv. Ann. Math.: Nouvelles Annales de Mathematiques. Journal des Candidats aux Ecoles Speciales,
a la Licence et a l'Agregation. Paris.
Nova Acta Acad. Sci. Petropol.: Nova Acta Academiae Scientiarum Imperialis Petropolitanae.
Par. Mem. Sav. (Etr.): Memoires Presentes par Divers Savants a l'Academie des Sciences de ^Insti-
tut de France. (Memoires des Savants Etrangers.). Paris.
Period. Mat.: Periodico di Mathematiche. Storia, Didattica, Filosofia. Bologna.
Phil. Mag.: The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science. London.
Phil. Trans. Roy. Soc. Lond; Philosophical Transactions of the Royal Society of London. (Series A.
Mathematical and Physical Sciences.).
Phys. Rev,: The Physical Review. A Journal of Experimental and Theoretical Physics... American
Physical Society. New York.
Portugaliae Math.: Portugaliae Mathematica. Lisbon.
Proc. Amer. Acad. Arts Sci: Proceedings of the American Academy of Arts and Sciences. Boston.
Proc. Akad. Wet. Amsterdam: K. Akademie van Wetenschappen, Amsterdam. Proceedings of the Section of
Sciences.
Proc. Camb. Phil. Soc: Proceedings of the Cambridge Philosophical Society.
Proc. Edin. Math. Soc: Proceedings of the Edinburgh Mathematical Society.
402
ABBREVIATIONS
^__. t-j »- aJ q„- . D», Cfi . e dir>»s Af t.he ]ndian Academy of Sciences. Section A. Hebbal, Bangalore,
Tn/1-i a .
Proc. Ind. Assoc. Sci.: Proceedings of the Indian Association for the Cultivation of Science. Cal-
cutta.
Proc. Lond. Math. Soc.: Proceedings of the London Mathematical Society.
Proc. Nat. Acad. Sci. U.S.A.: Proceedings of the National Academy of Sciences of the United States
of America. Washington, D. C.
Proc. Phys.-Math. Soc. Japan: Proceedings of the Physico-Mathematical Society of Japan. Faculty of
Science, Tokyo Imperial University.
Proc. Phys. Soc. Lond.: Proceedings of the Physical Society. London.
Proc. Roy. Soc. Edin.: Proceedings of the Royal Society of Edinburgh. (Section A. Mathematical and
Physical Sciences.).
Proc. Roy. Soc. Lond.: Proceedings of the Royal Society of London. Series A. Mathematical and Physi-
cal Sciences.
Proc. Tokyo Math.-Phys. Soc: Proceedings of the Tokyo Mathematico-Physical Society.
Publ. Inst. Mat. Univ. Nac. Litoral: Publicaciones del Instituto de Matematica. Facultad de Ciencias
Matematicas etc., de la Universidad National del Litoral.
Quart. Appl. Math.: Quarterly of Applied Mathematics. Providence, R. I.
Quart. Jour. Math.: The Quarterly Journal of Pure and Applied Mathematics. London. Superseded by The
Quarterly Journal of Mathematics, Oxford Series. Oxford.
Quart. Jour. Roy. Met. Soc: Quarterly Journal of the Royal Meteorological Society. London.
Rec. Math. (Mat. Sbornik): Academie des Sciences de l'URSS. Recueil Mathematique (Akademiia Nauk
Record Amer. Inst. Actuar.: The Record. American Institute of Actuaries. Chicago.
Rend. Accad, dei Lincei Roma: Atti della Reale Accademia Nazionale dei Lincei. Rendiconti. Classe di
Scienze, Fisiche, Matematiche e Naturali. Rome.
Rend. Circ Mat. Palermo: Rendiconti del Circolo Matematico di Palermo.
Rend. 1st. Lombardo: Reale Istituto Lombardo di Scienze e Lettere. Rendiconti. Milan.
Rend. Sem. Math. Fis. Milano: Rendiconti del Seminario Matematico e Fisico di Hilano.
Revista Ci. Lima: Revista de Ciencias. Organo de la Facultad de Ciencias de la Universidad Nacional
Mayor de San Marcos. Lima, Peru.
Revista Mat. Hisp.-Amer.: Revista Matematica Hispano-America. Publicada bajo los Auspicions de la
Sociedad Matematica Espanola y del Laboratorio-Seminario Matematico. Madrid.
Revista Union Mat. Argentina: Revista Union Matematica Argentina. Buenos Aires.
Revista Univ. Catolica Peru: Revista de la Universidad Catolica del Peru. Lima.
Rev. Sci. Instr.: The Review of Scientific Instruments. American Institute of Physics. New York.
Sankya: Sankya, The Indian Journal of Statistics. Calcutta.
Schr. Math. Sem. Inst. Angew. Math. Univ. Berlin: Schrif trades mathematischen Seminars und des In-
stituts fur angewandte Matheffiaiik an der Universxtat Bar^n.
403
ABBREVIATIONS
Sitzber. Akad, Wiss, Munchen: Akademie der Wissenschaften, Munchen. Sitzungsberichte der mathemati-
sch-naturiwissenschaftlichen AbteHung. Munich.
Sitzber. Akad. Wiss. Wien: Kaiserliche Akademie der Wissenschaften, Wien. Sitzungsberichte der math-
ematisch-naturwissenschaftliehen Klasse. Vienna.
Sitzber. Berl. Math. Ges.: Sitzungsberichte der Berliner Mathematischen Gesellschaft. (Published as
a supplement to Archiv der Mathematik und Physik, third series.).
Sitzber. bohm. Ges. Prag: Sitzungsberichte der Koniglichen Bohmischen Gesellschaft der Wissenschaf-
ten. Prague.
Sitzber. Heidelberg: Sitzungsberichte der Heidelbergen Akademie der Wissenschaften. Mathenatisch-
naturwissenschaftliche Klasse.
Skand. Aktuarietidskr. : Skandinavisk Aktuarietidskrift. Utgiven av den Banske Aktuarforening, Fin-
lands Aktuarforening, den Norske Aktuarforening och Svenska Aktuarforeningen. Uppsala.
Soc. Sci. Fennica. Comment. Phys-Math.: Societatis Scientiarum Fennica. Commentationes Physico-
Mathematicae. Helsingfors (Helsinki.).
Stockh. Akad. Forh.: 6fversigt af Kongl. Vetenskaps-Akademiens Forhandlingar . Stockholm.
Terr. Magnetism: Terrestrial Magnetism and Atmospheric Electricity. An International Quarterly
Journal. Baltimore, etc.
TShoku Math. Jour.: The Tohoku Mathematical Journal. The Tohoku Imperial University, Sendai.
Trans. Actuar, Soc. Amer.: Actuarial Society of America. Transactions. New York.
Trans. Amer. Math. Soc: Transactions of the American Mathematical Society. New York.
Trans. Amer. Soc. Civil Engrs.: Transactions of the American Society of Civil Engineers* New York.
Trans. Amer. Soc, Mech. Engrs,: American Society of Mechanical Engineers. Transactions.
Trans. Camb. Phil. Soc.: Transactions of the Cambridge Philosophical Society. Cambridge, Eng.
Trav. Inst. Math. Tbilissi (Trudy Tbiliss, Mat. Inst.): Akademiia Nauk SSSR Leningrad. Gruzinski
filial. Matematischeskii Institut, Trudy.
Uchenye Zapiski Moscov. Univ. Mat,: Uchenye Zapiski Moscovskogo Gosudarstvennogo Universiteta. Mos-
cow.
Univ.Nac, la Plata Publ, Fac, Ci. Fisicomat. Revista: Universidad Nacional de la Plata. Publicaciones
de la Faculdad de Ciencias Ffsicomatematicas. Contribution al Estudio de las Ciencias
Fisicas y Matema'ticas. Serie Tecnica. La Plata, Argentina.
Univ. Nac. Tucuman Revista: Universidad Nacional de Tucuman. Revista. Serie A, Matematicas y Fisica
Teorica. Tucuman, Argentina.
Zeit Angew. Math. Mech.: Zeitschrift fur angewandte Mathematik und Mechanik. Ingenieurwissenschaft-
liche Forschungsarbeiten. Berlin.
Zeit. Angew. Met,: Zeitschrift fur angewandte Meteorologie-Das Wetter. Mit Unterstutzung des Reich-
samts fur Wetterdienst,
Zeit. Instrument enkunde: Zeitschrift fur Lnstrumentenkunde. Organ fur Mitteilungen aus dem gesamten
Gebiete der wissenschaftlichen Technik. Berlin.
Zeit. Math. Naturwiss. Unterricht: Zeitschrift fur mathematische und naturwissenschaftliche Unter-
richt aller Schulgattungen. Leipzig.
Zeit. Math. Phys.: Zeitschrift fur Mathematik und Physik... Organ fur angewandte Mathematik, Leip-
zig.
404
ABBREVIATIONS
Zeit* Phy Sl . Zeitschriffc fur Physik, Herausgegeben unter Mitwirkung der Deutschen physikalischen Ges-
ellschaft. Berlin.
Zeit, VereLn. Deutsch. Ihg.: Zeitsehrift des Vereines Deutscher Ingenieure. Berlin.
405
INTRODUCTION TO THE APPENDICES
Chapter III discussed the operations of the various electrical components of the calculator. In
that discussion, the circuits were, for the sake of clarity, considerably abbreviated. Elements not
necessary to the understanding of the principle of operation of any section of the machine were omit-
ted. Where circuits are duplicated, either exactly or with minor modifications, usually only one of
the duplicated circuits was discussed. It is the purpose of these appendices to present, so far as
possible, the circuits as they actually occur, rather than their simplified forms heretofore employed.
These appendices are given on the pages indicated in the following table.
Appendix No.
Title
Page
I
Sequence Codes
Out Codes, A Relays
411
In Codes, B Relays
422
Miscellaneous Codes, C Relays
429
II
Sequence Circuits
Start, Stop, Repeat Circuits
431
Automatic Circuits
433
III
Register Circuits
Switch Circuits
437
Storage Counter Circuits
441
High Accuracy Circuits
446
Choice Counter Circuits
449
UIO Counter Circuits
451
Automatic Check Counter Circuits
455
IV
Multiply Unit Circuits
Multiplication
457
PQ Low Order Read-Out
494
Normalizing Register
495
7
Divide Unit Circuits
499
406
INTRODUCTION TO THE APPENDICES
Appendix No.
VI
VII
VIII
Title
Relay List
Multiply Divide Panel
Heavy Duty
Sequence
Switch
Storage Counter
Cam List
CC Cam Contacts
SC Cam Contacts
iff-DIV Fuse List
Page
528
545
546
546
547
550
554
555
J
Appendix I lists in tabular form the A, B and C relays energized by the reading of the various
sequence codes. Appendices II, III, IV and V indicate cycle by cycle the subsequent operations which
take place as a result of the pick up of these relays. In each of the appendices II, III, IV and V,
the following form is employed.
(a) The order in which the various relays are energized is stated in words.
fb) A timing diagram indicating that portion of the cycle during which each relay is energized
J 4- „*JZ w,o r^r-irtd of tine during which each relay is energized through its pick up cir-
cuirirshown bj a heavy bar covering the appropriate portion of the cycle. The period of
time during which the relay is energized through its hold circuit is indicated by an outline
bar.
(c) A circuit diagram is presented, showing graphically the pick up and hold circuits of each
relay. All relay points are shown in their normal (unenergized) positions.
Appendices VI, VII and VIII list the various relays, cams and fuses employed, together with the
purposes of each. Thus appendices I through V will enable the reader to trace an operation of the
calculator through the network of electric circuits involved, while appendices VI through VIII will
be useful in determining the purpose of a particular relay, cam or fuse.
From its inception to its completion, the circuits of the calculator have undergone a process of
constant evolution. In fact, changes are at the present time still being made. This is quite under-
standable, in view of the fact that the Automatic Sequence Controlled Calculator is the first general
purpose calculator to be successfully completed and put into operation. This series of changes has,
however, necessarily led to certain inconsistencies in the nomenclature of the various electrical
components of the calculator. To begin with, most of the electrical elements are designated by two
407
INTRODUCTION TO THE APPENDICES
separate names: first, a colloquial name brought about by common usage, such as "Q-control relay",
"X*s right relay", w DD-carry control relay", etc.; second, a specific numerical designation which is
the outgrowth of the originally logical system of numbering the various parts of the calculator* It
is this latter designation that will be discussed here.
(1) Relay Coil Designations
1. Except for a relatively few heavy duty relays, all relays in the calculator are of a stand-
ard type, of which six varieties are employed; namely:
4 point single coil 4 point double coil
6 point single coil 6 point double coil
12 point single coil 12 point double coil .
2. When a double coil relay is used, one coil serves for pick up, the other for hold.
3. The coils of these relays are designated according to their use in the calculator by a com-
bination of letters and numbers, usually consisting of a group of letters followed by three
groups of numbers. Each group is separated from the others by dashes, and the right hand
group is enclosed in parentheses; thus:
Seq-29-l-(l2), B-3-l,2,3-(l2).
4. The letter or group of letters on the left indicates the "section" of the machine in which
the relay is used. Sectional prefixes are given in the following tabulation.
Seq Sequence Relay
Swl, Sw2, ..., SwoO Switch Relay
A Code Selection Relay (Out Relay)
B Code Selection Relay (In Relay)
C Code Selection Relay (Miscellaneous Relay)
SCI, SC2, ..., SC72 Storage Counter Relay
Check Check Counter Relay
Choice Choice Counter Relay
Sp64, Sp65, Sp68, Sp69 Special Purpose Relay
CI Carry Interlock Relay
(none) MP-DIV or Functional Relay
In several places in the appendices, the relays associated with switch A are referred to by
the prefix SwA, and the relays associated with storage counter A by the prefix SCA.
5. An exception to this system of literal prefixes is the prefix HD. In general this denotes a
heavy duty relay, and thus refers to the type relay employed, not to its place in the cir-
cuits of the calculator. The single relay HD-3-l-(4) wc is, however, a wire contact rather
than a heavy duty relay, a fact denoted by the suffix we. This is the only relay prefixed
with HD that is not of the heavy duty type.
6. When it is required that more than 12 points operate simultaneously, a number of relays of
4, 6 or 12 points each are wired in parallel as a "bank". Reading from left to right, the
three groups of numbers in the relay designation denote respectively the number of the bank,
the numbers of the relays in the bank, and the number of points on each of these relays; thus:
(a) Seq-29-l-(12) denotes Sequence Relay Bank 29, one twelve point relay;
(b) B-3-l,2,3-(12) denotes Code Selection In, Bank 3, relays 1, 2 and 3, each of twelve
points.
7. As indicated in the tabulation of sectional prefixes, relays without literal prefix are ei-
ther MP-DIV or Functional relays. The banks of HP-DI7 relays are numbered 1 through 104.
The banks of functional relays are numbered from 100 consecutively upward. Thus there are
408
INTRODUCTION TO THE APPENDICES
two completely independent banks of relays for each of the bank numbers 100, 101, 102, 103
and 104.
8. When relays of varying numbers of points are employed in the same bank, any one of several
alternate designations may be used.
(a) Several lines may be employed.
Sw8-1,2-(12)
Sw8-3-(4) denotes Switch Bank 8, relays 1 and 2 each of 12 points and relay 3
of 4 points.
(b) If the relays of the different varieties occur periodically within the bank, several
of the numbers 4, 6 and 12 may be placed in the parentheses in the order in which the
corresponding relays recur; thus:
5-l,...,27-(12,12,4)
could be written in place of
5-1.2,4,5,7. 8.10,11,13,14. 16.17. 19.20. 22,23.25,26-(l2)
5-3,6,9,12,i5,18,21,24,27-(4) .
(c) Even though there is no periodicity in their recurrence, the relays of varying numbers
of points are sometimes written on one line; thus:
33-47,..., 70-(4,6 or 12).
This is a non-specific designation, since it does not give information as to which of
the 24 relays have 4, 6 and 12 points respectively. In order to give a specific desig-
nation in this case, it is necessary that several lines be used.
9. There is one and only one instance of a bank in which the individual relays are not numbered
consecutively. This is bank 29 of the MP-DIV panel. This bank has in addition to the 36
relays, 29-1, ...,36-(12, 12,6), a single 4 point relay designated as 29-9(2)-(4), which
operates with relay 29-9-(6).
(2) Relay Point Designations
1. In the interest of simplicity, the relay coils and their associated points are separated in
the following circuit diagrams. The designation of any relay point consists of a group of
letters followed by three groups of numbers, the groups being separated by dashes; thus:
C-l-11-11, Seq-32-1-2.
2. The letter or group of letters and the two groups of numbers on the left refer respectively
to the section, bank and individual relay in question. The number on the right denotes the
particular point of that relay. The letters NC or NO are often suffixed to the point des-
ignation to denote normally closed or normally open respectively; thus:
(a) C-1-11-11NC denotes the normally closed side of the 11th point of the 11th relay of
the 1st bank of the Miscellaneous relays of the code selection cascade;
(b) Seq-32-1-2 denotes the 2nd point of the 1st relay of the 32nd bank of the sequence
relays .
(3) Further Abbreviations
1. When only one relay is used in a bank, the number "one" of that relay will frequently be
omitted. Thus the relay Seq-31-l-(4) would be abbreviated to Seq-31-(4) . The designation
of the third point of this relay would be shortened from Seq-31-1-3 to Seq-31-3.
2. There are several instances of only one bank in a section of the calculator, and only one
409
INTRODUCTION TO THE APPENDICES
relay in that bank. In these cases, both bank numbers and relay numbers may be omitted.
Thus the relay Check-l-l-(4) is written Check-(4) and Choice-l-l-(6) is written Choice-(6).
Similarly, the 4th point of the check relay is written Check-4 and the third point of the
choice relay, Choice-3.
(4) Cam Designations
1. As explained in Chapter III, the timing of the various operations of the machine is control-
led by cam contacts. Three series of these cam contacts are used. They are distinguished
on the following diagrams and lists by the prefixed letters:
(a) CC denotes computing cam contacts (used principally for timing the operations of the
1AP-DIV unit);
(b) FC denotes functional cam contacts (used for timing the sequence and functional units);
(c) SC denotes storage cam contacts (used for timing impulses through the storage counters
and switches).
2. The number following this pair of letters denotes a particular cam of the series. The num-
bers in parentheses give the timing of the cam; thus:
(a) SC-11 (12-0) denotes storage cam contact number 11, makes at 12 time, breaks at time;
(b) CC-39 (1/3 15 - 12) denotes computing cam contact number 39, makes l/3 before 15 time,
breaks at 12 time.
3. Certain of the CC cams operate 16 times per cycle. In these cases, the letter L is used to
denote each one of the 16 subdivisions of the cycle in turn; thus:
(a) CC-23 (1/16 L - L 1/2) denotes cam contact number 23, makes 1/16 before line- breaks
1/2 after line; i.e.,
Makes Breaks
1/16 9 9 1/2
1/16 8 8 1/2
1/16 1/2
1/16*16 16*1/2.
4. Closely associated cams are given the same group number, but distinguished from each other
by a letter following that number; thus:
(a) CC-24B (L 1/4 - L 7/8) denotes B cam contact of group 24, makes 1/4 after line, breaks
7/8 after line.
(5) Designations of Other Electrical Elements
1. Counter Wheels
(a) The coils are clearly labeled counter magnet or Ctr. Mag.
(b) The spots or "read-outs" are numbered 0, 1, ..., 9 and labeled collectively ctr. R.O.
(c) Nines and tens carry contacts are labeled with a 9 and a 10 respectively.
2. Counter Registers
Names of registers are clearly given on the diagrams. The elements belonging to specific
component counter wheels are labeled col. 1, col. 2, ..., col. 24.
410
INTRODUCTION TO THE APPENDICES
3. Fuses
Fuses are prerixea er&ner witn i>ne j.et,&er r, ox- me ibwkmo «u , ^^xvumg, ~w ~~ ....- — -
they are mounted on the functional panel or on the MP-DIV panel. Each series is numbered
consecutively from one upward,
4. Binding Posts
Binding posts are divided into series each prefixed by VBP, SBP, FBP, BBP, VTP, ABPorSHBP.
Each series is numbered consecutively.
(6) Cycle Designations
1. Various functional operations extend over several cycles of the calculator. The multiple
cycle operations considered here are:
M Multiply
D Divide
NR Normalizing Register
Thus a relay would be said to operate in cycle D-6 if it were energized during the 6th cycle
of the division sequence of operations.
(7) Miscellaneous Symbols
1. Several special designations occur in Appendix VI. The letters S and D suffixed to the
relay designations denote respectively single coil and double coil. The numbers in the col-
umn headed "Row" refer to the physical rows of relays in the MP-DIV panel.
SEQUENCE CODES
The following table lists the cascade of relays which are involved in the reading of any given sequence code. The codes are tabulated ac-
cording to the sequence column, A, B or C, in which they are read. The first column of the table states the given code; the second, the
functional cam which provides the impulse; the third, the open points through which the impulse travels; the fourth, the normally closed
points through which the impulse travels; the fifth, the unit controlled by the sequence code.
OUT CODES- A RELAYS
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
1
92
1-1-1
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
3-1-1
2-1-1
Storage Counter #1- OUT
32
321
92
92
3-1-1
2-1-2
3-1-1
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
1-1-4
8-1-1
Storage Counter #6- OUT
2
92
2-1-1
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
2-1-2
1-1-4
7-1-1
6-1-1
5-1-1
4-1-1
Storage Counter #7- OUT
3-1-1
4
92
4-1-1
8-1-1
1-1-2
Storage Counter #2- OUT
7-1-1
6-1-1
21
92
2-1-1
1-1-2
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
5-1-1
3-1-2
2-1-3
1-1-5
Storage Counter #8- OUT
3-1-1
Storage Counter #3- OUT
41
92
4-1-1
1-1-5
8-1-1
7-1-1
3
92
3-1-1
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
6-1-1
5-1-1
3-1-2
2-1-3
Storage Counter #9- OUT
2-1-2
42
92
4-1-1
8-1-1
1-1-3
Storage Counter #4- OUT
2-1-3
7-1-1
6-1-1
31
92
3-1-1
1-1-3
8-1-1
7-1-1
6-1-1
5-1-1
5-1-1
3-1-2
1-1-6
Storage Counter #10- OUT
4-1-1
421
92
4-1-1
8-1-1
2-1-2
Storage Counter #5- OUT
2-1-3
1-1-6
7-1-1
6-1-1
OUT CODES- A RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
421
5-1-1
52
4-1-2
cont .
3-1-2
Storage Counter #11- OUT
cont.
3-1-3
1-1-10
Storage Counter #18- OUT
43
92
4-1-1
8-1-1
3-1-2
7-1-1
6-1-1
5-1-1
2-1-4
1-1-7
Storage Counter #12- OUT
521
92
5-1-1
2-1-5
1-1-10
8-1-1
7-1-1
6-1-1
4-1-2
3-1-3
Storage Counter #19- OUT
431
92
4-1-1
3-1-2
1-1-7
8-1-1
7-1-1
6-1-1
5-1-1
2-1-4
Storage Counter #13- OUT
53
92
5-1-1
3-1-3
8-1-1
7-1-1
6-1-1
4-1-2
2-1-6
1-1-11
Storage Counter #20- OUT
432
92
4-1-1
8-1-1
3-1-2
7-1-1
531
92
5-1-1
8-1-1
2-1-4
6-1-1
5-1-1
1-1-8
Storage Counter #14- OUT
3-1-3
1-1-11
7-1-1
6-1-1
4-1-2
2-1-6
Storage Counter #21- OUT
4321
92
4-1-1
8-1-1
3-1-2
7-1-1
532
92
5-1-1
8-1-1
2-1-4
6-1-1
3-1-3
7-1-1
1-1-8
5-1-1
Storage Counter #15- OUT
2-1-6
6-1-1
4-1-2
5
92
5-1-1
8-1-1
7-1-1
1-1-12
Storage Counter #22- OUT
6-1-1
5321
92
5-1-1
8-1-1
4-1-2
3-1-3
7-1-1
3-1-3
2-1-6
6-1-1
2-1-5
1-1-12
4-1-2
Storage Counter #23- OUT
1-1-9
Storage Counter #16- OUT
54
92
5-1-1
8-1-1
51
92
5-1-1
1-1-9
8-1-1
7-1-1
6-1-1
4-1-2
3-1-3
2-1-5
Storage Counter #17- OUT
541
92
4--1-2
5-1-1
7-1-1
6-1-1
3-1-4
2-1-7
1-2-1
8-1-1
Storage Counter #24- OUT
52
92
5-1-1
2-1-5
8-1-1
7-1-1
6-1-1
4-1-2
l-a-i
7-1-1
6-1-1
3-1-4
2-1-7
Storage Counter #25- OUT
OUT CODES- A RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
542
92
5-1-1
4-1-2
2-1-7
8-1-1
7-1-1
6-1-1
3-1-4
1-2-2
Storage Counter #26- OUT
61
cont.
62
92
6-1-1
2-1-9
3-1-5
2-1-9
8-1-1
7-1-1
5-1-2
Storage Counter #33- OUT
5421
92
5-1-1
4-1-2
2-1-7
1-2-2
8-1-1
7-1-1
6-1-1
3-1-4
Storage Counter #27- OUT
621
92
6-1-1
4-1-3
3-1-5
1-2-6
8-1-1
Storage Counter #34- OUT
543
92
5-1-1
4-1-2
3-1-4
8-1-1
7-1-1
6-1-1
2-1-8
1-2-3
Storage Counter #28- OUT
63
92
2-1-9
1-2-6
6-1-1
7-1-1
5-1-2
4-1-3
3-1-5
8-1-1
Storage Counter #35- OUT
5431
92
5-1-1
4-1-2
3-1-4
1-2-3
8-1-1
7-1-1
6-1-1
2-1-8
Storage Counter #29- OUT
3-1-5
7-1-1
5-1-2
4-1-3
2-1-10
1-2-7
Storage Counter #36- OUT
5432
92
5-1-1
8-1-1
4-1-2
7-1-1
631
92
6-1-1
8-1-1
3-1-4
6-1-1
3-1-5
7-1-1
2-1-8
1-2-4
Storage Counter #30- OUT
1-2-7
5-1-2
4-1-3
54321
92
5-1-1
4-1-2
8-1-1
7-1-1
2-1-10
Storage Counter #37- OUT
3-1-4
6-1-1
632
92
6-1-1
8-1-1
2-1-8
3-1-5
7-1-1
1-2-4
Storage Counter #31- OUT
2-1-10
5-1-2
4-1-3
6
92
6-1-1
8-1-1
7-1-1
5-1-2
4-1-3
3-1-5
2-1-9
1-2-5
Storage Counter #32- OUT
6321
64
92
92
6-1-1
3-1-5
2-1-10
1-2-8
6-1-1
1-2-8
8-1-1
7-1-1
5-1-2
4-1-3
8-1-1
Storage Counter #38- OUT
Storage Counter #39- OUT
61
92
6-1-1
1-2-5
8-1-1
7-1-1
5-1-2
4-1-3
4-1-3
7-1-1
5-1-2
3-1-6
CO
OUT CODES- A R ELAYS -continued-
Code
64
cont,
641
642
6421
643
PC
92
92
92
92
92
Open
6431
92
6432
92
64321
92
65
92
6-1-1
4-1-3
1-2-9
6-1-1
4-1-3
2-1-11
6-1-1
4-1-3
2-1-11
1-2-10
6-1-1
4-1-3
3-1-6
6-1-1
4-1-3
3-1-6
1-2-11
6-1-1
4-1-3
3-1-6
2-1-12
6-1-1
4-1-3
3-1-6
2-1-12
1-2-12
6-1-1
5-1-2
NC
2-1-11
1-2-9
8-1-1
7-1-1
5-1-2
3-1-6
2-1-11
8-1-1
7-1-1
5-1-2
3-1-6
1-2-10
8-1-1
7-1-1
5-1-2
3-1-6
8-1-1
7-1-1
5-1-2
2-1-12
1-2-11
8-1-1
7-1-1
5-1-2
2-1-12
8-1-1
7-1-1
5-1-2
1-2-12
8-1-1
7-1-1
5-1-2
8-1-1
7-1-1
4-1-4
Controls
Storage Counter #40- OUT
Storage Counter #41- OUT
Storage Counter #42- OUT
{Storage Counter #43- OUT
Storage Counter #44- OUT
Storage Counter #45- OUT
Storage Counter #46- OUT
Storage Counter #47- OUT
Code
65
cont.
651
652
6521
653
6531
6532
65321
654
FC
92
92
92
92
92
92
92
92
Open
6-1-1
5-1-2
1-3-1
6-1-1
5-1-2
2-2-1
6-1-1
5-1-2
2-2-1
1-3-2
6-1-1
5-1-2
3-1-7
6-1-1
5-1-2
3-1-7
1-3-3
6-1-1
5-1-2
3-1-7
2-2-2
6-1-1
5-1-2
3-1-7
2-2-2
1-3-4
6-1-1
5-1-2
NC
3-1-7
2-2-1
1-3-1
8-1-1
7-1-1
4-1-4
3-1-7
2-2-1
8--1-1
7-1-1
4-1-4
3--1-7
1-3-2
8-1-1
7-1-1
4-1-4
3-1-7
8-1-1
7-1-1
4-1-4
2-2-2
1-3-3
8-1-1
7-1-1
4-1-4
2-2-2
8-1-1
7-1-1
4-1-4
1-3-4
8-1-1
7-1-1
4-1-4
8-1-1
7-1-1
Controls
Storage Counter #48- OUT
Storage Counter #49- OUT
Storage Counter #50- OUT
Storage Counter #51- OUT
Storage Counter #52- OUT
Storage Counter #53- OUT
Storage Counter #54- OUT'
Storage Counter #55- OUT
OUT CODES- A RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
654
4-1-4
3-1-8
7
6-1-2
cont.
2-2-3
1-3-5
Storage Counter #56- OUT
cont*
5-1-3
4-1-5
3-1-9
6541
92
6-1-1
5-1-2
4-1-4
8-1-1
7-1-1
3-1-8
2-2-5
1-3-9
Storage Counter #64- OUT
1-3-5
2-2-3
Storage Counter #57- OUT
71
92
7-1-1
1-3-9
8-1-1
6-1-2
6542
92
6-1-1
5-1-2
4-1-4
8-1-1
7-1-1
3-1-8
5-1-3
4-1-5
3-1-9
2-2-3
1-3-6
Storage Counter #58- OUT
2-2-5
Storage Counter #65- OUT
65421
92
6-1-1
5-1-2
4-1-4
2-2-3
1-3-6
8-1-1
7-1-1
3-1-8
Storage Counter #59- OUT
72
92
7-1-1
2-2-5
8-1-1
6-1-2
5-1-3
4-1-5
3-1-9
1-3-10
Storage Counter #66- OUT
6543
92
6-1-1
8-1-1
5-1-2
7-1-1
721
92
7-1-1
8-1-1
4-1-4
2-2-4
2-2-5
6-1-2
3-1-8
1-3-7
Storage Counter #60- OUT
1-3-10
5-1-3
4-1-5
65431
92
6-1-1
5-1-2
8-1-1
7-1-1
3-1-9
Storage Counter #67- OUT
4-1-4
2-2-4
73
92
7-1-1
8-1-1
3-1-8
3-1-9
6-1-2
1-3-7
Storage Counter #61- OUT
5-1-3
4-1-5
65432
92
6-1-1
5-1-2
4-1-4
8-1-1
7-1-1
1-3-8
2-2-6
1-3-11
Storage Counter #68- OUT
3-1-8
731
92
7-1-1
8-1-1
2-2-4
Storage Counter #62- OUT
3-1-9
1-3-11
6-1-2
5-1-3
654321
92
6-1-1
5-1-2
4-1-4
8-1-1
7-1-1
4-1-5
2-2-6
Storage Counter #69- OUT
3-1-8
732
92
7-1-1
8-1-1
2-2-4
3-1-9
6-1-2
1-3-8
Storage Counter #63- OUT
2-2-6
5-1-3
4-1-5
7
92
7-1-1
8-1-1
1-3-12
Storage Counter #70- OUT
OUT COD'.SS- A RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
7321
92
7-1-1
3-1-9
2-2-6
8-1-1
6-1-2
5-1-3
74321
92
7-1-1
4-1-5
3-1-10
8-1-1
6-1-2
5-1-3
1-3-12
4-1-5
Storage Counter #71- OUT
2-2.-8
1-4-4
Switch #7- OUT
74
92
7-1-1
8-1-1
4-1-5
6-1-2
5-1-3
3-1-10
2-2-7
1-4-1
Storage Counter #72- OUT
75
92
7-1-1
5-1-3
8-1-1
6-1-2
4-1-6
3-1-11
2-2-9
1-4-5
Switch #8- OUT
741
92
7-1-1
8-1-1
4-1-5
6-1-2
751
92
7-1-1
8--1-1
1-4-1
5-1-3
3-1-10
2-2-7
Switch #1- OUT
5-1-3
1-4-5
6-1-2
4-1-6
3--1-11
2-2-9
Switch #9- OUT
742
92
7-1-1
4-1-5
2-2-7
8-1-1
6-1-2
5-1-3
3-1-10
1-4-2
Switch #2- OUT
752
92
7-1-1
5-1-3
2-2-9
8-1-1
6-1-2
4-1-6
3-1-11
1-4-6
Switch #10- OUT
7421
92
7-1-1
8-1-1
4-1-5
6-1-2
7521
92
7-1-1
8-1-1
2-2-7
5-1-3
5-1-3
6-1-2
4-1-6
3-1-11
1-4-2
3-1-10
Switch #3- OUT
2-2-9
1-4-6
Switch #11- OUT
743
92
7-1-1
8-1-1
4-1-5
3-1-10
6-1-2
5-1-3
2-2-8
1-4-3
Switch #4- OUT
753
92
7-1-1
5-1-3
3-1-11
8-1-1
6-1-2
4-1-6
2-2-10
1-4-7
Switch #12- OUT
7431
92
7-1-1
4-1-5
3-1-10
8-1-1
6-1-2
7531
92
7-1-1
8-1-1
5-1-3
5-1-3
6-1-2
1-4-3
2-2-8
Switch #5- OUT
3-1-11
1-4-7
4-1-6
2-2-10
Switch #13- OUT
7432
92
7-1-1
4-1-5
3-1-10
8-1-1
6-1-2
7532
92
7-1-1
8-1-1
5-1-3
5-1-3
6-1-2
2-2-8
_ _
1-4-4
Switch #6- OUT
3-1-11
2-2-10
4-1-6
1-4-8
Switch #14- OUT 1
OUT CODES- A RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
75321
92
7-1-1
5-1-3
3-1-11
2-2-10
1-4-8
8-1-1
6-1-2
4-1-6
Switch #15- OUT
754321
92
7-1-1
5-1-3
4-1-6
3-1-12
2-2-12
1-4-12
8-1-1
6-1-2
Switch #23- OUT
754
92
7-1-1
8-1-1
5-1-3
6-1-2
76
92
7-1-1
8-1-1
4-1-6
3-1-12
2-2-11
1-4-9
Switch #16- OUT
6-1-2
5-1-4
4-1-7
3-2-1
2-3-1
7541
92
7-1-1
5-1-3
8-1-1
6-1-2
1-5-1
Switch #24- OUT
4-1-6
3-1-12
761
92
7-1-1
8-1-1
1-4-9
2-2-11
Switch #17- OUT
6-1-2
1-5-1
5-1-4
4-1-7
7542
92
7-1-1
5-1-3
4-1-6
8-1-1
6-1-2
3-1-12
3-2-1
2-3-1
Switch #25- OUT
2-2-11
1-4-10
Switch #18- OUT
762
92
7-1-1
6-1-2
8-1-1
5-1-4
75421
92
7-1-1
5-1-3
4-1-6
2-2-11
8-1-1
6-1-2
3-1-12
2-3-1
4-1-7
3-2-1
1-5-2
Switch #26- OUT
1-4-10
Switch #19- OUT
7621
92
7-1-1
6-1-2
8-1-1
5-1-4
7543
92
7-1-1
8-1-1
2-3-1
4-1-7
5-1-3
6-1-2
1-5-2
3-2-1
Switch #27- OUT
4-1-6
2-2-12
3-1-12
1-4-11
Switch #20- OUT
763
92
7-1-1
6-1-2
8-1-1
5-1-4
75431
92
7-1-1
5-1-3
4-1-6
3-1-12
8-1-1
6-1-2
2-2-12
1-4-11
3-2-1
4-1-7
2-3-2
1-5-3
Switch #28- OUT
1-4-11
Switch #21- OUT
7631
92
7-1-1
6-1-2
8-1-1
5-1-4
75432
92
7-1-1
8-1-1
3-2-1
4-1-7
5-1-3
6-1-2
1-5-3
2-3-2
Switch #29- OUT
4-1-6
1-4-12
3-1-12
7632
92
7-1-1
8-1-1
2-2-12
Switch #22- OUT
6-1-2
5-1-4
OUT CODES- A RELAYS -continued-
Code
PC
Open
KC
Controln
1 7632
cont.
3-2-1
2-3-2
4-1-7
1-5-4
Switch #30- OUT
76321
92
7-1-1
6-1-2
3-2-1
2-3-2
1-5-4
8-1-1
5-1-4
4-1-7
Switch #31- OUT
764
92
7-1-1
6-1-2
4-1-7
8-1-1
5-1-4
3-2-2
2-3-3
1-5-5
Switch #32- OUT
7641
92
7-1-1
6-1-2
4-1-7
1-5-5
8-1-1
5-1-4
3-2-2
2-3-3
Switch #33- OUT
7642
92
7-1-1
6-1-2
4-1-7
2-3-3
8-1-1
5-1-4
3-2-2
1-5-6
Switch #34- OUT
76421
92
7-1-1
6-1-2
4-1-7
2-3-3
1-5-6
8-1-1
5-1-4
3-2-2
Switch #35- OUT
7643'
92
7-1-1
6-1-2
4-1-7
3-2-2
8-1-1
5-1-4
2-3-4
1-5-7
Switch #36- OUT
76431
92
7-1-1
6-1-2
4-1-7
3-2-2
1-5-7
8-1-1
5-1-4
2-3-4
.Switch #37- OUT
76432
92
7-1-1
6-1-2
4-1-7
8-1-1
5-1-4
1-5-8
00
Code
76432
cont.
764321
765
7651
7652
76521
7653
76531
76532
FC
92
92
92
92
92
92
92
92
92
Open
3-2-2
2-3-4
7-1-1
6-1-2
4-1-7
3-2-2
2-3-4
1-5-8
7-1-1
6-1-2
5-1-4
7-1-1
6-1-2
5-1-4
1-5-9
7-1-1
6-1-2
5-1-4
2-3-5
7-1-1
6-1-2
5-1-4
2-3-5
1-5-10
7-1-1
6-1-2
5-1-4
3-2-3
7-1-1
6-1-2
5-1-4
3-2-3
1-5-11
7-1-1
6-1-2
NC
8-1-1
5-1-4
8-1-1
4-1-8
3-2-3
2-3-5
1-5-9
8-1-1
4-1-8
3-2-3
2-3-5
8-1-1
4-1-8
3-2-3
1-5-10
8-1-1
4-1-8
3-2-3
8-1-1
4-1-8
2-3-6
1-5-11
8-1-1
4-1-8
2-3-6
8-1-1
4-1-8
Controls
Switch #38- OUT
Switch #39- OUT
Switch #40- OUT
Switch #41- OUT
Switch #42- OUT
Switch #43- OUT
Switch #44- OUT
Switch #45- OUT
OUT CODES- A RELAI3 -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
76532
5-1-4
1-5-12
-
765431
3-2-4
cont.
3-2-3
2-3-6
Switch #46- OUT
cont*
765432
92
1-6-3
7-1-1
8-1-1
Switch #53- OUT
765321
92
7-1-1
6-1-2
5-1-4
3-2-3
2-3-6
1-5-12
8-1-1
4-1-8
Switch #47- OUT
7654321
92
6-1-2
5-1-4
4-1-8
3-2-4
2-3-8
7-1-1
1-6-4
8-1-1
Switch #54- OUT
7654
92
7-1-1
6-1-2
5-1-4
4-1-8
8-1-1
3-2-4
2-3-7
1-6-1
Switch #48- OUT
6-1-2
5-1-4
4-1-8
3-2-4
2-3-8
76541
92
7-1-1
6-1-2
8-1-1
3-2-4
1-6-4
Switch #55- OUT
5-1-^4
2-3-7
8
92
8-1-1
7-1-2
4-1-8
6-1-3
1-6-1
Switch #49- OUT
5-1-5
4-1-9
76542
92
7-1-1
6-1-2
5-1-4
4-1-8
8-1-1
3-2-4
1-6-2
3-2-5
2-3-9
1-6-5
Switch #56- OUT
2-3-7
Switch #50- OUT
81
92
8-1-1
1-6-5
7-1-2
6-1-3
765421
92
7-1-1
6-1-2
5-1-4
4-1-8
2-3-7
8-1-1
3-2-4
5-1-5
4-1-9
3-2-5
2-3-9
Switch #57- OUT
1-6-2
Switch #51- OUT
82
92
8-1-1
2-3-9
7-1-2
6-1-3
76543
92
7-1-1
6-1-2
5-1-^4
4-1-8
3-2-4
8-1-1
2-3-8
1-6-3
Switch #52- OUT
821
92
8-1-1
5-1-5
4-1-9
3-2-5
1-6-6
7-1-2
Switch #58- OUT
765431
92
7-1-1
6-1-2
5-1-4
8-1-1
2-3-8
2-3-9
1-6-6
6-1-3
5-1-5
4-1-9
4-1-8
3-2-5
Switch #59- OUT
CO
OUT CODES- A RELAYS -continued-
So*.
to
MMM «W 'I 111-" •» ■■■' ■"
=>
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
83
92
8-1-1
7-1-2
8421
2-3-11
5-1-5
3-2-5
6-1-3
5-1-5
4-1-9
2-3-10
1-6-7
:3witch #60- OUT
cont.
843
92
1^5-10
8-1-1
4-1-9
3-2-6
3-2-6
7-1-2
6-1-3
5-1-5
2-3-12
Print Counter #2- Reset
831
92
8-1-1
3-2-5
7-1-2
6-1-3
1-6-11
Punch Counter- Reset
1-6-7
5-1-5
4-1-9
2-3-10
LI0- OUT (plugged)
8431
92
8-1-1
4-1-9
3-2-6
1-6-11
7-1-2
6-1-3
5-1-5
2-3-12
IVS- OUT
832
92
8-1-1
7-1-2
3-2-5
6-1-3
85
92
8-1-1
7-1-2
2-3-10
5-1-5
4-1-9
1-6-8
EIO- OUT
5-1-5
6-1-3
4-1-10
3-2-7
2-4-1
8323.
92
8-1-1
3-2-5
7-1-2
6-1-3
1-7-1
Interpolator #1- Read Ta]?e
2-3-10
5-1-5
851
92
8-1-1
7-1-2
1-6-8
4-1-9
Normalizing Register- OUT
5-1-5
1-7-1
6-1-3
4-1-10
84
92
8-1-1
4-1-9
7-1-2
6-1-3
5-1-5
3-2-6
2-3-11
1-6-9
SIO- OUT #2 (plugged)
852
92
8-1-1
5-1-5
2-4-1
3-2-7
2-4-1
7-1-2
6-1-3
4-1-10
3-2-7
Interpolator #2- Read Tape
841
92
8-1-1
4-1-9
7-1-2
6-1-3
1-7-2
Interpolator #3- Read Tape
1-6-9
5-1-5
3-2-6
2-3-11
"h" Correction to Intermediate Ctr.
853
92
8-1-1
5-1-5
3-2-7
7-1-2
6-1-3
4-1-10
2-4-2
MIO Counter-
842
92
8-1-1
4-1-9
7-1-2
6-1-3
1-7-3
Cols. 13-24 to Buss Cola. 13-24
2-3-11
5-1-5
3-2-6
1-6-10
Print Counter #1- Reset
8531
92
8-1-1
5-1-5
3-2-7
1-7-3
7-1-2
6-1-3
4-1-10
2-4-2
MIO Counter-
Cols. 13-24 to Buss Cols. 1-12
842].
92
8-1-1
4-1-9
7-1-2
6-1-3
OUT CODES- A RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
86
92
8-1-1
7-1-2
8731
3-3-1
4-2-1
6-1-3
5-1-6
4-1-11
3-2-9
2-4-5
1-7-9
PQ Counter- Cols. 1-23 Product-Out
cont.
8732
92
1-9-3
8-1-1
7-1-2
3-3-1
2-5-2
2-5-2
6-Ln4
5-1-7"
4-2-1
1-9-4
Typewriter #1- OFF
Typewriter #2- OFF
862
92
8-1-1
7-1-2
6-1-3
5-1-6
874
92
8-1-1
6-1-4
2-4-5
4-1-11
3-2-9
1-7-10
Print Counter #1- OUT
7-1-2
4-2-1
5-1-7
3-3-2
2-5-3
1-9-5
SIO- OUT #1 (plugged)
8621
92
8-1-1
7-1-2
6-1-3
5-1-6
8741
92
8-1-1
6-1-4
2-4-5
4-1-11
7-1-2
5-1-7
1-7-10
3-2-9
Print Counter #2- OUT
4-2-1
1-9-5
3-3-2
2-5-3
SIO- OUT #3 (direct)
863
92
8-1-1
6-1-3
3-2-9
7-1-2
5-1-6
4-1-11
2-4-6
1-7-11
Punch Counter- OUT
87
92
8-1-1
7-1-2
6-1-4
5-1-7
4-2-1
3-3-1
2-5-1
1-9-1
Argument Control
871
92
8-1-1
7-1-2
1-9-1
6-1-4
5-1-7
4-2-1
3-3-1
2-5-1
Typewriter #1- ON
872
92
8-1-1
7-1-2
2-5-1
6-1-4
5-1-7
4-2-1
3-3-1
1-9-2
Typewriter #2- ON
8731
92
8-1-1
7-1-2
6-1-4
5-1-7
CO
IN CODBE i- B RELAYS
Code
FG
Open
NC
Controls
Code
FC
Open
NC
Controls
1
93
1-1-1
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
321
cont*
2-1-2
1-1-4
7-1-1
6-1-1
5-1-1
4-1-1
Storage Counter #7- IN
3-1-1
4
93
4-1-1
8-1-1
2-1-1
Storage Counter #1- IN
7-1-1
6-1-1
2
93
2-1-1
8-1-1
7-1-1
6-1-1
5-1-1
4-1-1
5-1-1
3-1-2
2-1-3
1-1-5
Storage Counter #8- IN
3-1-1
41
93
4-1-1
8-1-1
1-1-2
Storage Counter #2- IN
1-1-5
7-1-1
6-1-1
21
93
2-1-1
1-1-2
8-1-1
7-1-1
6-1-1
5-1-1
5-1-1
3-1-2
2-1-3
Storage Counter #9- IN
4-1-1
42
93
4-1-1
8-1-1
3-1-1
Storage Counter #3- IN
2-1-3
7-1-1
6-1-1
3
93
3-1-1
8-1-1
7-1-1
6-1-1
5-1-1
5-1-1
3-1-2
1-1-6
Storage Counter #10- IN
4-1-1
421
93
4-1-1
8-1-1
2-1-2
2-1-3
7-1-1
1-1-3
Storage Counter #4- IN
1-1-6
6-1-1
5-1-1
31
93
3-1-1
1-1-3
8-1-1
7-1-1
3-1-2
Storage Counter #11- IN
6-1-1
43
93
4-1-1
8-1-1
5-1-1
3-1-2
7-1-1
4-1-1
6-1-1
2-1-2
Storage Counter #5- IN
5-1-1
2-1-4
32
93
3-1-1
2-1-2
8-1-1
7-1-1
1-1-7
Storage Counter #12- IN
6-1-1
431
93
4-1-1
8-1-1
5-1-1
3-1-2
7-1-1
4-1-1
1-1-7
6-1-1
1-1-4
Storage Counter #6- IN
5-1-1
2-1-4
Storage Counter #13- IN
321
93
3-1-1
8-1-1
IN CODES- £ RELAYS -continued-
Code
FC
432
4321
93
93
93
51
93
52
93
521
53
93
93
Open
4-1-1
3-1-2
2-1-4
4-1-1
3-1-2
2-1-4
1-1-8
5-1-1
5-1-1
1-1-9
5-1-1
2-1-5
5-1-1
2-1-5
1-1-10
5-1-1
3-1-3
NC
8-1-1
7-1-1
6-1-1
5-1-1
1-1-8
8-1-1
7-1-1
6-1-1
5-1-1
8-1-1
7-1-1
6-1-1
4-1-2
3-1-3
2-1-5
1-1-9
8-1-1
7-1-1
6-1-1
4-1-2
3-1-3
2-1-5
8-1-1
7-1-1
6-1-1
4-1-2
3-1-3
1-1-10
8-1-1
7-1-1
6-1-1
4-1-2
3-1-3
8-1-1
7-1-1
6-1-1
4-1-2
2-1-6
1-1-11
Controls
Storage Counter #14- IN
Storage Counter #15- IN
Code
Storage Counter #16- IN
Storage Counter #17- IN
Storage Counter #18- IN
Storage Counter #19- IN
Storage Counter #20- IN
531
532
5321
54
FC
93
93
93
93
5U
542
5421
543
93
93
93
93
Open
NC
5-1-1
8-1-1
3-1-3
7-1-1
1-1-11
6-1-1
4-1-2
2-1-6
5-1-1
8-1-1
3-1-3
7-1-1
2-1-6
6-1-1
4-1-2
1-1-12
5-1-1
8-1-1
3-1-3
7-1-1
2-1-6
6-1-1
1-1-12
4-1-2
5-1-1
8-1-1
4-1-2
7-1-1
6-1-1
3-1-4
2-1-7
1-2-1
5-1-1
8-1-1
4-1-2
7-1-1
1-2-1
6-1-1
3-1-4
2-1-7
5-1-1
8-1-1
4-1-2
7-1-1
2-1-7
6-1-1
3-1-4
1-2-2
5-1-1
8-1-1
4-1-2
7-1-1
2-1-7
6-1-1
1-2-2
3-1-4
5-1-1
8-1-1
4-1-2
7-1-1
3-1-4
6-1-1
2-1-8
1-2-3
Controls
Storage Counter #21- IN
Storage Counter #22- IN
Storage Counter #23- In
Storage Counter #24- In
Storage Counter #25- IN
Storage Counter #26- IN
Storage Counter #27- IN
Storage Counter #28- IN
IN CODES- B RELAYS -continued-
Code
VC
5431
5432
54321
93
93
93
93
61
93
62
93
Open
621
63
93
93
5-1-1
8-1-1
4-1-2
7-1-1
3-1-4
6-1-1
1-2-3
2-1-8
5-1-1
8-1-1
4-1-2
7-1-1
3-1-4
6-1-1
2-1-8
1-2-4
5-1-1
8-1-1
4-1-2
7-1-1
3-1-4
6-1-1
2-1-8
1-2-4
6-1-1
8-1-1
7-1-1
5-1-2
4-1-3
3-1-5
2-1-9
1-2-5
6-1-1
8-1-1
1-2-5
7-1-1
5-1-2
4-1-3
3-1-5
2-1-9
6-1-1
8-1-1
2-1-9
7-1-1
5-1-2
4-1-3
3-1-5
1-2-6
6-1-1
8-1-1
2-1-9
7-1-1
1-2-6
5-1-2
4-1-3
3-1-5
6-1-1
8-1-1
3-1-5
7-1-1
NC
Controls
Storage Counter #29- IN
Storage Counter #30- IN
Storage Counter #31- IN
Storage Counter #32- IN
Storage Counter #33- IN
Storage Counter #34- IN
Storage Counter #35- IN
Code
63
cont.
631
632
6321
64
641
642
6421
FC
93
93
93
93
93
93
93
4».
CO
Open
6-1-1
3-1-5
1-2,-7
6-1-1
3-1-5
2-1-10
6-1-1
3-1-5
2-1-10
1-2-8
6-1-1
4-1-3
6-1-1
4-1-3
1-2-9
6-1-1
4-1-3
2-1-11
6-1-1
4-1-3
2-1-11
1-2-10
NC
5-1-2
4-1-3
2-1-10
1-2-7
8-1-1
7-1-1
5-1-2
4-1-3
2-1-10
8-1-1
7-1-1
5-1-2
4-1-3
1-2-8
8-1-1
7-1-1
5-1-2
4-1-3
8-1-1
7-1-1
5-1-2
3-1-6
2-1-11
1-2-9
8-1-1
7-1-1
5-1-2
3-1-6
2-1-11
8-1-1
7-1-1
5-1-2
3-1-6
1-2-10
8-1-1
7-1-1
5-1-2
3-1-6
Controls
Storage Counter #36- IN
Storage Counter #37- IN
Storage Counter #38- IN
Storage Counter #39- IN
Storage Counter #40- IN
Storage Counter #41- IN
Storage Counter #42- IN
Storage Counter #43- IN
IN CODES- B RELAYS -continued-
Code
FC
643
6431
6432
64321
65
93
93
93
93
93
651
652
65a
93
93
93
Open
NC
6-1-1
8-1-1
4-1-3
7-1-1
3-1-6
5-1-2
2-1-12
1-2-11
6-1-1
8-1-1
4-1-3
7-1-1
3-1-6
5-1-2
1-2-11
2-1-12
6-1-1
8-1-1
4-1-3
7-1-1
3-1-6
5-1-2
2-1-12
1-2-12
6-1-1
8-1-1
4-1-3
7-1-1
3-1-6
5-1-2
2-1-12
1-2-12
6-1-1
8-1-1
5-1-2
7-1-1
4-1-4
3-1-7
2-2-1
1-3-1
6-1-1
8-1-1
5-1-2
7-1-1
1-3-1
4-1-4
3-1-7
2-2-1
6-1-1
8-1-1
5-1-2
7-1-1
2-2-1
4-1-4
3-1-7
1-3-2
6-1-1
8-1-1
5-1-2
7-1-1
2-2-1
4-1-4
1-3-2
3-1-7
Controls
Storage Counter #44- IN
Storage Counter #45- IN
Storage Counter #46- IN
Storage Counter #47- IN
Storage Counter #48- IN
Storage Counter #49- IN
Storage Counter #50- IN
Storage Counter #51- IN
Code
653
6531
6532
65321
654
6541
6542
65421
FC
93
93
93
93
93
93
93
93
Open
6-1-1
5-1-2
3-1-7
6-1-1
5-1-2
3-1-7
1-3-3
6-1-1
5-1-2
3-1-7
2-2-2
6-1-1
5-1-2
3-1-7
2-2-2
1-3-4
6-1-1
5-1-2
4-1-4
6-1-1
5-1-2
4-1-4
1-3-5
6-1-1
5-1-2
4-1-4
2-2-3
6-1-1
5-1-2
4-1-4
2-2-3
1-3-6
NC
8-1-1
7-1-1
4-1-4
2-2-2
1-3-3
8-1-1
7-1-1
4-1-4
2-2-2
8-1-1
7-1-1
4-1-4
1-3-4
8-1-1
7-1-1
4-1-4
8-1-1
7-1-1
3-1-8
2-2-3
1-3-5
8-1-1
7-1-1
3-1-8
2-2-3
8-1-1
7-1-1
3-1-8
1-3-6
8-1-1
7-1-1
3-1-8
Controls
Storage Counter #52- IN
Storage Counter #53- IN
Storage Counter #54- IN
Storage Counter #55- IN
Storage Counter #56- IN
Storage Counter #57- IN
Storage Counter #58- IN
Storage Counter #59- IN
to
Jai
IN C0J3ES- £ R ELAYS -continued-
Code
FC
6543
65431
65432
654321
93
93
93
93
93
71
93
72
93
Open
NC
6-1-1
8-1-1
5-1-2
7-1-1
4-1-4
2-2-4
3-1-8
1-3-7
6-1-1
8-1-1
5-1-2
7-1-1
4-1-4
2-2-4
3-1-8
1-3-7
6-1-1
8-1-1
5-1-2
7-1-1
4-1-4
1-3-8
3-1-8
2-2-4
6-1-1
8-1-1
5-i-a
7-1-1
4-1-4
3-1-8
2-2-4
1-3-8
7-1-1
8-1-1
6-1-2
5-1-3
4-1-5
3-1-9
2-2-5
1-3-9
7-1-1
8-1-1
1-3-9
6-1-2
5-1-3
4-1-5
3-1-9
2-2-5
7-1-1
8-1-1
2-2-5
6-1-2
5-1-3
4-1-5
3-1-9
1-3-10
Controls
Code
Storage Counter #60- IN
Storage Counter #61- IN
Storage Counter #62- IN
Storage Counter #63- IN
721
73
Storage Counter #64- IN
(Storage Counter #65- IN
Storage Counter #66- IN
731
732
7321
74
FC Open
93
93
741
7432
93
93
93
93
93
93
7-1-1
2-2-5
1-3-10
7-1-1
3-1-9
7-1-1
3-1-9
1-3-11
7-1-1
3-1-9
2-2-6
7-1-1
3-1-9
2-2-6
1-3-12
7-1-1
4-1-5
7-1-1
4-1-5
IhW.
7-1-1
4-1-5
NC
8-1-1
6-1-2
5-1-3
4-1-5
3-1-9
8-1-1
6-1-2
5-1-3
4-1-5
2-2-6
1-3-11
8-1-1
6-1-2
5-1-3
4-1-5
2-2-6
8-1-1
6-1-2
5-1-3
4-1-5
1-3-12
8-1-1
6-1-2
5-1-3
4-1-5
8-1-1
6-1-2
5-1-3
3-1-10
2-2-7
1-4-1
8-1-1
6-1-2
5-1-3
3-1-10
2-2-7
8-1-1
6-1-2
to
J0»
Controls
Storage Counter #67- IN
Storage Counter #68- IN
Storage Counter #69- IN
Storage Counter #70- IN
Storage Counter #71- IN
Storage Counter #72- IN
EIO- IN
IN CODES- B RELAYS -continued-
Code
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
7432
3-1-10
5-1-3
7621
95
7-1-3
8-1-2
cont.
2-2-8
1-4-4
Print Counter #1- IN
6-1-5
2-3-1
5-1-4
4-1-7
74321
93
7-1-1
4-1-5
8-1-1
6-1-2
1-5-2
3-2-1
Exponential
3-1-10
5-1-3
763
95
7-1-3
8-1-2
2-2-8
6-1-5
5-1-4
1-4-4
Print Counter #2- IN
3-2-1
4-1-7
2-3-2
752
93
7-1-1
5-1-3
8-1-1
6-1-2
1-5-3
Interpolate
2-2-9
4-1-6
3-1-11
1-4-6
Typewriter #1- Initiate Printing
7631
95
7-1-3
6-1-5
3-2-1
1-5-3
8-1-2
5-1-4
4-1-7
2-3-2
Sine
7521
93
7-1-1
8-1-1
5-1-3
6-1-2
7654
95
7-1-3
8-1-2
2-2-9
4-1-6
6-1-5
3-2-4
1-4-6
3-1-11
Typewriter #2- Initiate Printing
5-1-4
4-1-8
2-3-7
1-6-1
Select Interpolator #1
753
93
7-1-1
8-1-1
5-1-3
6-1-2
765U
95
7-1-3
8-1-2
3-1-11
4-1-6
2-2-10
1-4-7
Punch Counter- IN
6-1-5
5-1-4
4-1-8
1-6-1
3-2-4
2-3-7
Select Interpolator #2
76
95
7-1-3
8-1-2
6-1-5
5-1-4
4-1-7
3-2-1
2-3-1
1-5-1
Divide
76542
95
7-1-3
6-1-5
5-1-4
4-1-8
2-3-7
8-1-2
3-2-4
1-6-2
Select Interpolator #3
761
95
7-1-3
6-1-5
1-5-1
8-1-2
5-1-4
4-1-7
3-2-1
2-3-1
Multiply
765421
95
7-1-3
6-1-5
5-1-4
4-1-8
2-3-7
1-6-2
8-1-2
3-2-4
LIO- IN
762
95
7-1-3
8-1-2
6-1-5
5-1-4
76543
95
7-1-3
8-1-2
2-3-1
4-1-7
3-2-1
1-5-2
Logarithm
6-1-5
5-1-4
4-1-8
3-2-4
2-3-8
1-6-3
Print Counter #1- Half Pick-up
IN RELAYS- B RELAYS - continued-
Code
FC
Open
765431
95
8321
853
8531
87
93
93
93
93
871
873
873]-
93
93
93
NC
7-1-3
8-1-2
6-1-5
2-3-8
5-1-4
4-1-8
3-2-4
1-6-3
8-1-1
7-1-2
3-2-5
6-1-3
2-3-10
5-1-5
1-6-8
4-1-9
8-1-1
7-1-2
5-1-5
6-1-3
3-2-7
4-1-10
2-4-2
1-7-3
8-1-1
7-1-2
5-1-5
6-1-3
3-2-7
4-1-10
1-7-3
2-4-2
8-1-1
6-1-4
7-1-2
5-1-7
4-2-1
3-3-1
2-5-1
1-9-1
8-1-1
6-1-4
7-1-2
5-1-7
1-9-1
4-2-1
3-3-1
2-5-1
8-1-1
6-1-4
7-1-2
5-1-7
3-3-1
4-2-1
2-5-2
1-9-3
8-1-1
6-1-4
7-1-2
5-1-7
3-3-1
4-2-1
1-9-3
2-5-2
Controls
Print Counter #2- Half Pick-up
Normalizing Register- IN
MIO Counter- IN
Buss Cols. 13-24 to MIO Cols. 13-24
MIO Counter- IN
Buss Cols. 1-12 to MIO Cols. 13-24
Storage Counter #64- Special IN
Storage Counter #65- Special IN
Storage Counter #68- Special IN
Storage Counter #69- Special IN
Code
874
8741
FC
93
93
Open
8-1-1
7-1-2
4-2-1
8-1-1
7-1-2
4-2-1
1-9-5
CO
NC
6-1-4
5-1-7
3-3-2
2-5-3
1-9-5
6-1^4
5-1-7
3-3-2
2-5-3
Controls
SIO- IN #1 (direct)
SIO- IN #2 (plugged)
MISCELLANEOUS CODES- C RELAYS
Code
FC
21
94
94
94
31
32
321
432
94
94
94
94
94
Open
1-1-1
2-1-1
2-1-1
1-1-2
94 3-1-1
3-1-1
1-1-3
3-1-1
2-1-2
3-1-1
2-1-2
1-1-4
4-1-1
3-1-2
2-1-4
5-1-1
NC
6-1-1
5-1-1
4-1-1
3-1-1
2-1-1
6-1-1
5-1-1
4-1-1
3-1-1
1-1-2
6-1-1
5-1-1
4-1-1
3-1-1
6-1-1
5-1-1
4-1-1
2-1-2
1-1-3
6-1-1
5-1-1
4-1-1
2-1-2
6-1-1
5-1-1
4-1-1
1-1-4
6-1-1
5-1-1
4-1-1
6-1-1
5-1-1
1-1-8
6-1-1
4-1-2
3-1-3
2-1-5
1-1-9
Controls
Storage Counter- Read-Out
Negative Absolute Value
Storage Counter- Read-Out
Positive Absolute Value
Switch- Invert
Intermediate Counter- Reset
EIO- Reset
Storage Counter and Switch- Invert
SIO- Reset
Read-Out Under Control of
Counter #70
Initiate Punching
Code
51
53
531
532
54
541
542
61
62
FC
94
94
94
94
94
94
94
96
96
96
Open
NC
5-1-1
1-1-9
6-1-1
4-1-2
3-1-3
2-1-5
5-1-1
3-1-3
6-1-1
4-1-2
2-1-6
1-1-11
5-1-1
3-1-3
1-1-11
6-1-1
4-1-2
2-1-6
5-1-1
3-1-3
2-1-6
6-1-1
4-1-2
1-1-12
5-1-1
4-1-2
6-1-1
3-1-4
2-1-7
1-2-1
5-1-1
4-1-2
1-2-1
6-1-1
3-1-4
2-1-7
5-1-1
4-1-2
2-1-7
6-1-1
3-1-4
1-2-2
6-1-2
5-1-2
4-1-3
3-1-5
2-1-9
1-2-5
6-1-2
1-2-5
5-1-2
4-1-3
3-1-5
2-1-9
6-1-2
2-1-9
5-1-2
4-1-3
3-1-5
1-2-6
Controls
Initiate and Complete Punching
Interpolator #1- Step Ahead
Interpolator #2- Step Ahead
Interpolator #3- Step Ahead
Interpolator #1- Step Back
Interpolator #2- Step Back
Interpolator #3- Step Back
Print and Complete Printing
Interpolation- Drop out
Tape Selection Relays
Pick up Interpolation-
Sequence Control Relay
ilk.
to
MISCELLANEOUS CODES- C RELAYS -continued-
Codle
FC
Open
NC
Controls
Code
FC
Open
NC
Controls
63
96
6-1-2
3-1-5
5-1-2
4-1-3
2-1-10
1-2-7
LIO- Reset
87
106
8-1-1
7-1-2
Stop- with Stop Key
632
96
6-1-2
3-1-5
2-1-10
5-1-2
4-1-3
1-2-8
Card Feed #1- OUT
6321
96
6-1-2
3-1-5
2-1-10
1-2-8
5-1-2
4-1-3
Card Feed #2- OUT
64
96
6-1-2
4-1-3
5-1-2
3-1-6
2-1-11
1-2-9
Automatic Check
641
96
6-1-2
4-1-3
1-2-9
5-1-2
3-1-6
2-1-11
Interpolator- Position
643
96
6-1-2
4-1-3
3-1-6
5-1-2
2-1-12
1-2-11
Division- Place Limitation
6431
96
6-1-2
4-1-3
3-1-6
1-2-U
5-1-2
2-1-12
Division- Place Limitation
6432
96
6-1-2
4-1-3
3-1-6
2-1-12
5-1-2
1-2-12
Division- Place Limitation
64321
96
6-1-2
4-1-3
3-1-6
2-1-12
1-2-12
5-1-2
Division- Place Limitation
7
107
106
7-1-1
7-1-3
Repeat
Stop- with Jinergency Switch and
£»top Key-
SEQUENCING - START . STOP . REPEAT
The start key is depressed and the start relay energized. Through the start relay, the read control relay, the start interlock relay and
the clutch magnet are energized. The sequence mechanism reads the line of coding (A, B, 7) • The corresponding sequence relays including
C-7 and thus the repeat relay are picked up. The pick up of the start interlock relay will open the circuit through the start key to the
start relay, preventing the flow of current to the start relay in the event that the start key is held down. If the repeat relay is ener-
gized, the start relay will pick up. If the emergency switch is on and the stop key depressed, the energized sequence relay C-7 will
permit the stop control relay to pick up. The pick up of stop control opens the circuit to the read control relay and the clutch magnet.
The stop control relay may also be picked up through the stop key and points of sequence relays C-8 and C-7«
Magnet
Seq-33-1 Start
Seq-31-1 Read Control
Clutch Magnet
Seq-28-1 Start Interlock
Seq-C-7-1
Seq-27-1 Repeat
Seq-32-1 Stop Control
Cycle
Cycle 1
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
Start Key or
Seq-27-1-1
VBP-276
FC-103 (6-5 1/3)
VBP-277
Seq-27-1-2
Seq-28-1-1 NC
FC-105 (4-2 1/2)
Sequence Cut-off
Switch
Card Feed ffl Sw.
Card Feed #2 Sw.
BBP-64
Seq-33-1-1
Seq-32-1-1,2 NC
Seq-27-1-1 or
Start Key
VBP-276
FC-104 (3-2 1/2)
VBP-279
Seq-33-1-3
Seq-33-l-(4)
Start
FC-108 (6-2 1/2)
VBP-278
Seq-33-1-4
± Start Key~" ^,Sea-2 7-l-l
1 FC-10 3 (6-5 1/3) .Seq-2 7-1-2
hfnrfc. I T V
"VB?2276' H~
.FC-10 8 (6-2 1/2)
fc T_J
*=±— ct
VBP^277
Seq-31-l-(4)
Read Control
and Clutch
Magnet
Seq-28-l-(4)
Start Interlock
VBTC278 "■
+ . FC-1 05 (4-2 1/2)
,£63=33-1-4
__ - F-18
Start
Seq-33-l-(4)
m
s~
v~
Y~
. . . . . . „ oSsg-33-l-l
Seq.Sw. C.F.#1 Sw. C.F.#2 Sw. BBP^64^ ♦ T Seo-3 2-l-l
Clutch
Magnet
^F-19
Seq-27-1-1 or
Start Key
VBP-276
Seq-28-1-4
+ „ Seq-2 7-1-1
— o — — *—
- F-18
Read Control
Seq-31-l-(4)
* -
Start Key
FC-10 4 (3-2 1/2)
"VBP=276~
H . , Q Seq- 33-l-3
VBPi579 »
Seq-2 8-1-4
- F-18
StarT'lnterlock
Seq-28-l-(4)
SEQUENCING - STAR T. STOP . REPEAT -continued-
Pick Up Circuit
FC-101 (3-2 1/3)
VBP-IOO
Seq-31-1,2,3,4
Reading Pins
Magnet
C-7-1-U)
FC-107 (0-5 1/4)
VBP-280
C-7-1-1
Stop Key
VBP-281
FC-106
(12-13 1/3)
VBP-282
C-7-1-3
Emergency Sw.
FC-101 (3-2 1/3)
VBP-100
Seq-31-1,2,3,4
Reading Pins
Seq-27-l-(4)
Repeat
Seq-32-l-(4)
Stop Control
C-8-l-(4)
C-7-l-(4)
Stop Key
VBP-281
FC-106
(12-13 1/3)
VBP-282
C-7-1-2
C-8-1-1
Seq-32-l-(4)
Stop Control
Hold Circuit
FC-102 (4-9 3A)
VBP-225
C-7-1-4
FC-107 (0-5 1/4)
VBP-280
Seq-27-1-4
Stop Key
VBP-281
Seq~32-l-4
FC-102 (4-9 3/4)
VBP-225
C-8-1-4
C-7-1-4
Circuit Diagram
Stop Key
VBP-281
S«iq~32-l-4
+JE-101 (3-2 1/3)
S&
VBP-100
.FC-102 (4-9 3/4)
VBTCZ25
t
,Seq-31-2
t
,Seq-31-3
f t
[Seq-31-4
t
i
£:7
9-
C-7-1-4
^5^fc?J" 18
_+ FC-107 (0-5 1/4)
TT . ^ . _c-7-i-i
msm-
- F-
Seq-27-1-4 rT?epea^"
Seq-27-l-(4)
+ Stop Key
~~R". „ .FC-10 6 (12-13 1/3)
•"^VBPfeeir' ^TT , ~ J3-7-1-3
TOP=282
Seq-32-1-4
Emer.Sw.
^/-le
Stop Control
Seq-32-l-(4)
+ FC-10 1 (3-2 1/3)
H ->
P^^-9
Seg.-31-l
VBP-100
Seq-3 1-2
^eg^l-3
Seq-31-4
FC-1C2 (4-9 3/4)
JC-8
C-8^1-4
C~7
£-7^1-4
i-aJL- 1
■ F-18
C-8-l-(4)
C-7-l-(4)
VBP-225
+■ Stop Key
FC-106 (12-13 1/3)
p-7-1- 2
^F-18
Stop* Control
Seq-32-l-(4)
SEQUENCING - AUTOMATICS
As mentioned on page 15, the code Miscellaneous 7 which controls the repeat relay may be replaced by certain automatic continue operation
codes. The circuits controlled by these automatic codes are presented in the following table, except for the circuit operated by the check
code, Miscellaneous 64, which is included in the automatic check counter circuits. Each of these circuits may replace the circuit through
the start relay to pick up the read control relay and the clutch magnet. For all automatic codes, the cam contact FC-105 provides the im-
pulse which travels through the card feed control circuits, as shown in the card feed circuit, to BBP-64. The alternate circuits employed
by the automatic codes of the different components of the machine are shown between BBP-64 and FBP-98. All of the circuits are completed
from FBP-98 to the read control relay and the clutch magnet as shown in the last diagram of this group.
Pick Up Circuit
NC
NC
NC
NC
BBP-64
12-1,2-3
or
BBP-110
44-5-1
BBP-111
FBP-133
216-1-2
and
55-3-2
78-2-8
81-2-9
BBP-52
FBP-99
201-1-2 NC
FBP-98
BBP-64
79-1-7
48-1-7
BBP-54
or
BBP-110 and
165-1-8
290-1-2 NC or
162-1-7
130-1-2 NC
176-1-2 NC or
254-3-1
255-3-1
256-1-2
257-1-2
and
FBP-98
Magnet
Hold Circuit
Circuit Diagram
MULTIPLY-DIVIDE UNIT
+s-0 ol2=l-3
BBP.
64
=2.-3
o55=3-2
^T . q81-2-9
I ^ FBP^- 9 9 q201 -1 -2
BBPC52 °^ ^^
BBP-110 + _._ p o_Z§P^ 133 2l6-l -2
BBP-111
Ofcs— &
FBpV§8~
INTERPOLATION UNIT
■. ~ „79-l- 7
BBP^4~° r , ^8-1- 7
o— — <y
BBP=llCr
FBP - 98 t -
Pick Up Circuit
BBP-64
11.-1-5
34-3-8(not used)
BBP-54
or
BBP-110
FBP-135
207-1-1
and
FBP-98
BBP-64
12-1,2-3
or
BBP-110
^-5-1
BBP-111
FBP-133
216-1-2 NC
or
FBP-135
266-3-1
217-3-1
216-1-3
and
55-3-2 NC
78-2-8 NC
81-2-9 NC
BBP-52
FBP-99
201-1-2 NC
or . ...
216-1-2
225-1-3 NC
FBP-181
BBP-53 ....
or
22A-3-1
and
FBP-98
SEQUEN CE - AUTOMATIC -continued-
CO
Magnet
Hold Circuit
Circuit Diagram
LOG UNIT
11-1-5
BBP$110
-o34=2r*
(not used) BBP^
ift-s s
ymm
?k
FBP*135 t _
EXPONENTIAL UNIT
+. n - 12-1-3
BBPfoTT
' 12-2-3
-3.-2
"f 5 ^
, 78-2- 8
^~T , -81-2-9
"^T . ~ FBPj99 -201-1 -2
BBP^52 T .
FBP*$
^4-5-1
BBP¥110~" \
2l6-lc2_
FBPfijT \ Q 2l6-l -3
212=2-1
t
Q 224- 3-l
_ 225-J-3
"FBP^8T
Pick Up Circuit
BBP-64
81-3-1 NC
230-3-3
FBP-98
BBP-64
BBP-110
FBP-135
113-3-2
112-1-3
103-3-1
102-3-12
143-3-2
142-1-3
133-3-1
132-3-12
100-1-2
FBP-98
BBP-64
BBP-110
FBP-135
246-3-2
248-1-11
or
Card Indicator-
1,2 NC
245-3-2
and
FBP-98
SEQUENCING - AUTOMATICS -continued-
Magnet
Hold Circuit
Circuit Diagram
BBP^64
bIp264~
SINE UNIT
Jl=2rl
BBP-^4
tL
,220=3-3
FBP=98
PRINT
BBP*110
FBP-135
012=3-2
♦
,112-1-3
♦ ,
,102-3-1
t .
,102-3-12
♦
143-2-2
♦ ,
142-1-3
♦ .
,133-3-1
f .
100-1-2
132-3-12
♦
♦ . >
W&W*
PUNCH
+ s^ IBP^llO
FBP-135
,246-3-2
.248-1-11
Card Indicator-1
Card Indicator-2
,245-3-2
TBl^g- e
4k.
CO
en
SEQUENCIN G - AUTOMATICS -continued-
W
CD
Pick Up Circuit
FC-105 (4-2 1/2)
Sequence Cut-off
Switch
Seq-25-1-1,2
Seq-26-1-1,2
Card. Feed #1 Sw,
Card Feed #2 Sw.
BBP-64
Magnet
Hold Circuit
FBP-98
Seq-32-1-1 NC
Seq-32-1-2 NC
Seq-31-l-(4)
Read Control
and
Clutch Magnet
Circuit Diagram
CARD FEED
jtJ&ADH (4-2 1/2)
TT. V oSfiar25-l-l
Seq.Sw.
t
^Seq- 25-1-2
y~
-Sea=26-1-1
t_
£©^26-1-2
/
C.F.#1 Sw. C.F„#2 Sw.
( Completion of Preceding Circuits )
,^§3-32-1-2
Read Control
S<sq-31-l-(4)
_ - F-18
r\ — F— 19
~ v ^*~^Clutch Magnet
BBP^64
SWITCHES
CYCLE 0. Assuming it is desired to read out of switch 8, code 75, into storage counter 5, code 31, the sequence mechanism reads the line
of coding (75, 31, blank). The sequence relays are picked up. The switch 8 out and storage counter 5 in relays are energized. If the code
32 is used in the Miscellaneous column, the storage counter invert relay is picked up. If the code 21 is used in the Miscellaneous column,
the switch invert relay and the IVS invert relay are picked up. If the code 8431 in the Out column is read, the independent variable
switch (IVS) out relays are energized.
CYCLE 1. The storage counter magnets are energized. The carry circuits, which are presented under storage counters, are closed and the
carry impulse completes the entry.
Magnet
Seq-A-7-1
Seq-A-5-1
Seq-B-3-1,2,3
Seq-B-l-l,..,ll
SC5-4,5,6 Str Ctr In
Sw8-1,2,3 Switch Out
Str Ctr Magnets
Seq-C-2-1, . . ,6
Seq-C-1-1, ..,11
Switch Invert
Seq-A-8-1
Seq-A-4-1,2
Seq-A-3-1,2,3
Seq-A-l-l,..,ll
Seq-30-1,2,3 IVS Out
Seq-29-1 IVS Invert
Cycle
Cycle 1
I I I
■ I I I I
Pick Up Circuit
FC-101 (3-2 1/3)
VBP-100
Seq-31-1,2,3,4
Reading Pins
Magnet
A-7-l-(4)
A-5-l-(12)
B-3-l,2,3-(12)
B-l-l,..,ll-(12)
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
A-7-1-4
A-5-1-11
B-3-3-11
B-l-11-11
Circuit Diagram
4 FC-10 1 (3-2 1/3)
* H . Q pSea=31-l
VBP-100
Seq-31-2
Seq-3 1-3
Seq-31-4
{ ^=LL
< «^
FC-10 2 (4-9 3/4)
H vBp g^r —
* J i ^=L
A-7-1-4
+su
A-5
^-5-1-11 — r^A^-l-
A-7-l-(4)
- F-16
■(12)
3-3-3-11 I^iB-3-l,2,3-(12)
t
r P-17
B-l-1 1-11 p^B^-1 . . . f 11-(12)
SWITCHES -continued-
Pick Up Circuit
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1 NC
A-7-1-1
A-6-1-2 NC
A-5-1-3
A-4-1-6 NC
A-3-1-11 NC
A-2-2-9 NC
A-l-4-5 NC
SwBP-2-8
SC-1,..,9
Str Ctr Reset NC
Str Counter
Invert NC
SBP-3-l,..,9
swbp-:l-i,..,9
Switch Invert NC
SwBP-1-11,.,,20
Switch RO
Sw8-1,2 Sw Out
Buss
SC5-4,5
Str Ctr In
FC-101 (3-2 3/3)
VBP-lOO
Seq-31-1,2,3,4
Reading Pins
Magnet
Sw8-1,2-(12)
Sw8-3-(4)
SC-11 (12-0)
SBP-1-2
SwBP-3-28
Sw8-3-4
Str Counter
Magnets
- w ,...5-(12)
-2-6-(6)
C-l-l,..,ll-(12) IC-1-11-11
C-2-1,
C
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
C-2-6-6
oo
Circuit Diagram
+ FC-92 (12 1/2-13 2/3)
CK-i=8-l-l
f _«£=5=l-3
t__JW4-l-6 Switch Out
-^X^A-3^11
I 0^=2-2-9
SC-11 (12-0) [
H
SBP-1-2 SwBP-3-28
^w8-3-4
+ SC-1. .,>.9
-H p. — !
Sw8-3-(4)
- F-14
Str Ctr f . q.
Reset Str Ctr " SBP-3- SwBP^l^ -0 F
ire — * g._ ^h <J^
Invert 1,..,9 1 #»-,9 Switch 'SwBPi3£~
Invert 11, . . ,20
6 l o 2°3 o 4° 5 6°7 8°9
Sw RO ^ jSwS-1 ,2
SC5-4,5
3
F-14
+ FC-101 (3-2 1/3)
"^Hl^-^^^^sja^i-i
VBP-lOO
Seq-3 1-2
t_
5egt21-3
fet31-4
FC-10 2 (4-9 3/4)
fiJP^225
■ * * K z^h
,C-2
Buss
*SLi
*SU~
Str Counter
.C-l
C-2-6-6
9-
t
[C-l-11-11
t _
C-2-1,.., 5-(12)
C-2-6-(6)
]^C^i,..,ll-(l2)
SWITCHES -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
SC-1,..,9
Str Ctr Reset NC
Str Counter
Invert NC
SBP-3-l,..,9 and
SBP-6-10
SwBP-l-l,..,9
Switch Invert NC
SwBP-l-ll,..,20
Switch Common
and RO
+ SC-1
.SC-2
SC-3
SC-4
SC-5
SC-6
H o.
SC-7
SC-8
SC-9
Str Ctr Reset
* -
XI
t__
Str Ctr Invert
"L^
"L_
* -
T—
T_i
X~I
J—*
t_^£°.
SBP
3A
Switch Invert R.O.
Mldgs.
4 -
^s^p—f
1-1 ' ^
3-2 *
25 W"T~Z
a5 S?zr-T
3 o^-^
3-6 ♦
3 -^r-[
3-8 *
- j52 i9r^TT
SwBP
^4 *,
^cH 2
1-13 3
— ch* 6-
i^cM
1-;
& £
i^dt
1-17 7
— o-V d-
* — 0—» O—
2^S.
• — o— fr o—
SWITCHES -continued-
it*
o
Pick Up Circuit
FC-94
(12 1/2-13 2/3)
VBP-H8
c-6-i-i n
C-5-1-1 N
C-4-1-1 N
C-3-1-1 N
C-2-1-1
C-l-1-2
SBP-1-9
SwBP-3-26
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1
A-7-1-2 NC
A-6-1-3 NC
A-5-1-5 NC
A-4-1-9
A-3-2-6
A-2-3-12 NC
A-l-6-11
FC-1,..,9
FBP-33,..,49
VBP-267,..,275
Seq-29-1 NC
IVS W
Seq-30-1,2
Buss
SC5-4,5
FC-94
(12 1/2-13 2/3)
VBP-148
C-6-1-1
C-5-1-1
C-4-1-1
C-3-1-1
C-2-1-1
C-l-1-2
NC
NC
NC
NC
Magnet
Switch Invert
Seq-30-l,2-(12)
Seq-30-3-(4)
IVS-OUT
Str Counter
Magnets
Seq-29-l-(12)
IVS Invert
Hold Circuit
SC-11 (12-0)
SBP-1-2
SwBP-3-28
Sw Invert-11
FC-97 (12-0)
VBP-173
Seq-30-3-4
FC-97 (12-0)
VBP-173
Seq-29-1-12
Circuit Diagram
±,FC-94 (12 1/2-132/3)
.C-6-1-1
VBP^548*^ T n C-5-l -l
^^L_^=4-i-i
^T_ < £r3j^-1
t SC-ll (12-0)
H . o . n ■ o 5 " ln vert-11
SBP5-2 SwBP-3-28 + ,
T C-2-l-l
tL_ Czkl-2
Sw Invert-(12)
-Q
SBP-1-9 SwBF
m^]
+ FC-92 (12 1/2-13 2/5)
"H",. >.8-l-l
VBF550 7 .A-7-1- 2
"SwlP^3-3'0 SBP%-9"*F^l4
Seq-30-l,2-(12)
Seq-30-3-(4)
IVS-OUT
FC-97 (12-0)
VBF3773
r£ecfc30-3-4
t__oA-2-2-12
] F-18
±jre^..,9
=0^77=0-
Sea-29";1
F13P^37T . ,49 VBP^6T
,..,275
o l o 2 o 3 o 4Y5 o 6 o 7 o 8 o 9°
IVS RO I jSeq-3 0-1.2
t . o 0505=4,5
Buss t silr<l> F " 14
erMaenet
+FC-94 (12 1/2-13 2/3)
a
__. ^-6-1-1
VBP^T T C-5-l- l
T" c-4-i-i
^T_ 43 S=3-J-l
L_oe=2-i-i
J FC-9 ?. (12-0) t C-l-l -2
T3_, n— ^ Se a= 29-l-12 t
Str Counter Magnets
IVS Invert
'VBI&173
t
r^H^tai)
r F-18
STORAGE COUNTERS
CYCLE 0. Assuming that is is desired to read out of storage counter 3, code 21, into storage counter 1, code 1, the sequence mechanism
reads the line of coding (21, 1, blank). The sequence relays are picked up. The storage counter 3 out and storage counter 1 in relays are
energized. If the code 1 in the Miscellaneous column is read, an additional circuit is closed, if a stands in the 24th column of counter
3, picking up the storage counter invert relay and thus causing the negative absolute value to be read out. If the code 2 in the Miscella-
neous column is read, an additional circuit is closed, if a 9 stands in the 24th column of counter 3, picking up the storage counter invert
relay and thus causing the positive absolute value to be read out. Assuming that it is desired to reset counter 1, the sequence mechanism
reads the line of coding (1, 1, blank). The storage counter 1 out and in relays and the storage counter reset relays are picked up. The
energizing of the storage counter reset relay opens the circuit to the carry control relay.
CYCLE 1. The storage counter magnets are energized. The storage counter carry control, carry and 24th column carry relays are picked up.
The carry impulse completes the storage counter entry.
Magnet
Seq-A-2-1, . . ,6
Seq-A-l-l,..,ll
Seq-B-l-l,..,ll
SC3-1,2,3 Storage Counter Out
SCl-4,5,6 Storage Counter In
Storage Counter Magnets
SC1-9 Storage Counter Carry Control
SCl-7,8 Storage Counter Carry
SCl-10,11 24th Column Carry
SC3-10,11 24th Column Carry
Storage Counter Invert
Str Ctr Invert (- Absolute Value)
Str Ctr Invert (+ Absolute Value)
Storage Counter Reset
Pick Up Circuit
FC-101 (3-2 1/3)
VBP-100
Seq-31-1, 2,3,4
Reading Pins
Magnet
A-2-l,..,5-(12)
A-2-6-(6)
A-1-1,..,11-(12)
B-l-l,..,ll-(12)
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
A-2-6-6
A-l-11-11
B-l-11-11
Cycle
Cycle 1
I I
Circuit Diagram
+ FC-101 (3-2 1/3)
+SU,
A-2-l,...5-(12)
l-2-6-(6)
- F-16
A-l-l,..,ll-(12)
^S^l,..,ll-(12)
Ts&m
STORAGE COUNTERS -continued-
Pick i[Jp Circuit
Magnet
Hold Circuit
Circuit Diagram
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1 NC
A-7-1-1 NC
A-6-1-1 NC
A-5-1-1 NC
A-4-1-1 NC
A-3-1-1 NC
A-2-1-1
A-l-1-2
SBP-10-3
Storage Ctr Out
SC3-1,2-(12)
SC3-3-U)
SC-11 (12-0)
SBP-l-2
SC3-3-4
+ FC-92 (12 1/2-13 2/3)
. H >- o„. oibft-i-i
iffiP-150 T o A -7;l-l
T A-6-3.-
ISC-U (12-0)
H ,_^ oSC3=3-4 '
SBF3.-2 f
■1
A-5-l-l
T .A-4-1-1 Str Ctr Out
T oA-2-i-i
T A-2-1-1
t A-l-l-2
*~1
1 -
. .- F-14
SBP-10-3 1 SU3-1,2-(12)
SC3-3-(4)
FC-93
(12 1/2-13 2/3)
VBP-H9
B-8-1-1 NC
B-7-1-1 NC
B-6-1-1 NC
B-5-1-1 NC
B-4-1-1 NC
B-3-1-1 NC
B-2-1-1 NC
B-1-1-1
SBP-8-1
Storage Ctr In
SCl-4,5-(12)
SCl-6-(4)
SC-U (12-0)
SBP-l-2
SC1-6-4
+ FC-93 (12 1/2-13 2/3)
^^mttpp f 3-7-1-1
T J3-6-1-
— W"
SC-11 (12-0)
""FT. ~ . J5C1-6-4
•1
B-5-1-1
r B-4-1-1 Str (
t n B-3-l-l
° f .B-2-1-1
J
3tr In
-1-1
^ r F-14
"SBP-l-2" " f
* SBP2e-l T "501^4, 5-112)
SCl-6-(4)
SC-1,..,9
Str Ctr Reset NC
Str Counter
Invert NC
SBP Rows 3,.., 7
Str Ctr RO
SC3-1,2 Str Ctr
Out
Buss
SCl-4,5 Str Ctr
In
Storage Ctr
Magnets
+ <
m^.,9 —
" . •
Str Ctr Reset f
<~v
Str Ctr Invert SBP~Rowe
3 7
Posts 1°2 3 4 5 6 7T8 9° „SC3-1,2-1,».,12
1,..,10 Str Ctr RO
1—.
«SCl-i
+ , 5-1,.., 12
StrCount<
Magnets
F-14
Bubs " +
Sr* "
STORAGE COUNTERS -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
SC-1,..,9
Str Ctr Reset NC
Str Counter
Invert NC
SBP Rows 3,.., 7
Str Counter
RO Moldings
rrr .o (
^
sc-:
a
Str Ctr Reset
SC-2
I_
T . ,
SC-,
a-
SC-5
s.
SC-6
,SC-8
SC-9
H^
Str Ctr Invert
a
SBP Rows RO
3,.., 7 Moldings
^ — °3"
"^ — * °4
^ — * °5
■^ — • — * V
^ *— ' °7"
^§ • — - °r
^ 9
-O- • » o—
35
Pick Up Circuit
SC-13 (2-1 1/2)
Reset-10 NC
SBP-1-4
SC1-6-1
SC-12 (11-14)
SBP-1-3
SC1-9-1
SC-12 (11-14)
SBP-1-3
SC1-9-2
9 or 10 Contact
SC-15 (13-15 1/3)
SBP-1-6
SC3-3-1
9 or 10 Contact
FC-94
(12 1/2-13 2/3)
VBP-148
C-6-1-1 NC
C-5-1-1 NC
C-4-1-1 NC
C-3-1-1
C-2-1-2
C-l-1-4 NC
SBP-1-12
FC-100
(13-15 1/4)
Seq-10-1-1
SC-17(14-14 1/2)
SBP-].-10
SC3-H-2 NC
SC3-3-3
SBP-1-12
Magnet
Str Ctr Carry-
Control
SCl-9-(4)
Str Ctr Carry
SCl-7,8-(12)
24th Col Carry
SCl-ll-(4) or
-10-(4)
SC1-
24th Col Carry
SC3-ll-(4) or
SC3-10-(4)
Str Ctr Invert-
(12)
Hold Circuit
Invert (Minus
Absolute RO)-
(12)
SC-14
(2-14 1/16)
SBP-1-5
SC].-9-4
SC--11 (12-0)
Invert-12
SC--11 (12-0)
Invert-12
STORAGE COUNTERS -continued-
Circuit Diagram
» SC-13 (2-1 1/2)
H . Jteset -10
J=L -^ cpS± T „ .SC1-6 -1
SC-14 (2-14 1/16)
TT rv J5C1-9 -4
w _^ >rF-14
SCi-9^4)
Str Ctr Carry
Control
+ SC-12 (11-14)
~~ TT n -SC1-9-1
- L - J - t ~SBP^E-^ ° r _^~. F-14
*~^-S~Cl377$:(i2) Str Ctr Carry
+ SC-12 (11-14)
- F-14
rt SC1-9-2 _^ 9JT
^T 3 Cl^fl-(4) 24th Col Carry
'^^ SCl-10-(4)
+ SC-15 (13-15 1/3) , <t ^*~<J-U
~"TT n . SC3-3-1 n 9f OL T3c3^L-(4)
t< ^i SC3 _ 10 _ (4)
+ FC-94 (12 1/2-13 2/3)
TT ^^ c-6-1-1
'WP^lSS^T C-5-1-1
°"— y- c-3-1-1
-° T c-2-1-2
T — O'
24th Col Carry
SC-11 (12-0)
^Hl
c-1-1-4
Invert-12
T
Str Ctr Invert
- F-14
S^l=12>^nv^rt-(:L2)
+ FC-100 (13-15 1/4)
seq-10-1-1
°— -*— sc-17 (14-14 1/5T 1 * . JSC3-3-3
^^H
SC3-11-2
-o— — o-
SC-11 (12-0)
TBI
-sBpfcccr
Minus Absolute R0
- F-14
* SBlfcl2>%nVe:rt-(12)
Invert-12
-o-
STORAGE COUNTERS -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
FC-100
(13-15 1/4)
Seq-11-1-1
SC-18(14-14 1/2)
SBP-1-11
SC3-11-2
SC3-3-3
SBP-1-12
SC-16
(14-15 1/3)
SBP-1-7
SC1-6-2
SC1-3-2
SBP-2-12
SC-10
(12-12 1/2)
SBP-1-1
Str Ctr Carry
Contacts
SCl-7,8-l,..,12
SC1-11,10-1
Invert (Plus
Absolute RO)-
(12)
Str Counter
Reset-(12)
Str Counter
Magnets
5C-11 (12-0)
Invert-12
SC-11 (12-0)
Reset-12
+ , FC-10 (13-15 1/4)
w
=11 (12-0)
Sea-11 -1-1 SC3- 11-2
t . .SC-ie (14-14 J72VI Q SC3-3-^
H . Q. ^ * t_
SBP^l-11
Plus Absolute RO
^_F-14
£nvert-(12)
-» — o — —
SBP^l-12
^
Jnxsrt-12
f , SC-16 (14-15 1/3)
H . q_^SC1-6-2
sBP-iPr r
LSC-ll (12-0)
a
^01=3-2
Str Ctr Reset
pReset -12
+ SC-10 (12-12 1/2)
* |_|
M » ^>
.SC1-12-2
SBP-1-1
SC1-12-;
9K.
_10f
9£
jloj
9£
_iQt
^01=7-2
t_, ^UPol.2
9£
lOf
.SC1-1 3-2
sci-13-3
9£
SCl-11-1
* —
SC1 -10-1%
J3arry Booster-
"^ 12.(4)
^Cl-7 -12
* . J^.Col.12
♦ - «jU Co1 - 13
„SCl-8-ll
t_^__^.Col.23
JSC1-8-12
_^ n .Carry Booster-
"^13-(4)
*MjS34
- F-14
Str Ctr Magnets
en
HIGH ACCURACY
CYCIE 0. Assuming that it is desired to read from register R into storage counter 68, code 73, ldth the ganged carry control, the sequence
mechanism reads the line of coding (R, 873, blank). The sequence relays are picked up. The storage counter 68 in relay and the special
storage counter 68 in relay are picked up.
CYCIE 1. Through the special storage counter 68 in relay, the carry interlock relay, ganging the carry circuits of counter 68 and 69, is
picked up.
CO
Magnet
Seq-B-8-1
Seq-B-7-1
5eq-B-3-l,2,3
Sp68-In
SC68-In
Storage Counter Magneta
Carry Interlock-2
SC68-9 Carry Control
SC69-9 Carry Control
SC68-7,8 Carry
SC69-7,8 carry
Cycle
Cycle 1
Pick Up Circuit
FC-101 (3-2 1/3)
VBP-100
Seq-31-1,2,3,4
Reading Pins
Magnet
B-8-l-m
B-7-l-(4)
B-3-l,2,3-(l2)
FC--102 (4-9 3/4)
VBP-225
B-13-1-4
B-7-1-4
B-3-3-11
Hold Circuit
Circuit Diagram
» FC-10 3. (3-2 1/3)
^HL^ n Se 3= 31-l
\ r BP-100
Seq-31-2
Sea-31-3
Jgeq-31-4
t_
.B-8
T — *SU
8-1-4
«££
«c2=l-
FC-102 (4-9 3/4)
-Tl^^25"
r *SL
U
B-8-l-(4)
3j^hll
t_l
B-7-l-(4)
_- F-17
B-3-l,2,3-(l2)
HIGH ACCURACY -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1
B-7-1-2
B-6-1-4 NC
B-5-1-7 NC
B-4-2-1 NC
B-3-3-1
B-2-5-2 NC
B-l-9-3 NC
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1
B-7-1-2
B-6-1-4
B-5-1-7
B-4-2-1
B-3-3-1
B-2-5-2
B-l-9-3
Sp68-1
Sp68-IN-(4)
SC68-4,5-(12)
SC68-6-(4)
SC-13 (2-1 1/2)
Reset-10 NC
SBP-2-4
Sp68-3
Sp69-3
SC-13 (2-1 1/2)
Reset-10 NC
SBP-2-4
SC68-6-1
SC-13 (2-1 1/2)
Reset-10 NC
SBP-2-4
SC69-6-1
Carry Interlock-
2-(6)
Carry Control
SC68-9-(4)
Carry Control
SC69-9-(4)
SC-11 (12-0)
SBP-2-2 and
SC68-6-4
Sp68-1 or
Sp68-4
SC-11 (12-0)
SBP-2-2
SC68-6-4
sc-14
(2-14 1/16)
SBP-2-5
C 1-2-6
SC-14
(2-14 1/16)
SBP-2-5
SC68-9-4
SC-14
(2-14 1/16)
SBP-2-5
SC69-9-4
+,Ffr- ?3 (12 1/2-13 2/3)
Q qB— 8— 1 — 1
VBP-149 ♦ qB-7-1-2
\ pB-6-1-4
ISCJJL (12-0)
, q . qSCoQ— 6— L
SBP-2-2
T__oB=5=l-7 Special Str Ctr IN
I <B=4=2-1 Sp68-IN-(4)
w T qB-3-3-1
,Sp68-l + B-2-5 -2
f qB-3li9-3 F-14
t ^JL^-o
_oSb68-4
+ .FC-9,3 (12 1/2-13 2/3)
H r^rB-e-1-1
VBP^549 r qB-7-1-2
t oE=6=l-4
t fi-5-1 -7 Normal Str Ctr IN
f gB-4-2-1 SC68-4,5-(12)
^~y ^-3-3-1 SC68-6-(4)
SC-11 (12-0)
SBP-2-2
* SC-13 (2-1 1/2)
st-10
qSC68-6-4
f qB-1-9-3
F-14
cm&rl
i-14 (2-14 1/16) SBP-2-4
SC-14 (2-14 l/li
H . ' o- — ♦
Jfipd2-3
-CI-2- 6
SBP-2-5
4 SC-13 (2-1 1/2)
H , Jteset -10
gC^ (2-14 1/16) T . Q
H=T . Q i ^SC68- 9-4 SBP^T
sbp-2-5 r ,
•», SC-13 (2-1 1/2) C
H , ^ Reset -10
^068- 6-1
T
<^F-14
Carry Inter lock-2-(6)
Str Ctr Carry Control
SC68-9-(4)
-c F-14
-c£I=2r5
T~ t Q ^C6Q- 6-l
SC-14 (2-14 1/16) SBP^-4 ♦ .
H . D __^ o SQ69-9-4
SBP32-5 4 ,
1<U—C,F-14
Str Ctr Carry Control
SC69-9-U)
HIGH ACCURACY -continued-
SC-10
(12-12 1/2)
SBP-2-1
Str Ctr Carry
Contacts
SC68-7-l,..,12
SC69~8-1,..,12
SC68--11,10-1
SC69«7-1,..,12
SC69'-8-l,.„,12
SC69»11,10.-1
Pick Up Circuit
Magnet
Counter Magnets
Ctrs 68 and 69
Hold Circuit
Circuit Diagram
±_JC=10 (12-12 1/2)
FT ,»
SBP-2-1
col.l 9_£
l ot
col.2 9^
10 •
col. 23 9jE
10_f
SC68-11-1
SC6 8-10-3J
col. 24
-£I=2>3
C 1-2-4
col.l 9jE
l°J
col.2 9jT
l°J
col.23 9 * ~
SC69-11-1
i —
SC69 -10-3%
CI-2- 1
" 1_
n-2-2
_r
col. 24
Counter 68
SC68-7~1
J L . ^Q.^ col. 1
-oSCita-7-2
t— ,JL
,SC68-8-ll
SC68-8-12
t_
SC69-7-2
SC69-8-11
,SC69-8»12
-J^
-Jlx
Counter 69
_ SC69-7-l
* . K^
-sJL-
-vk-
col. 2
col. 23
col. 24
col. 1
col. 2
col. 23
^Jcol. 24
CHOICE COUNTER
CYCLE 0. The sequence mechanism reads the Miscellaneous code 432 and picks up the corresponding sequence relays. The choice relay of
counter 70 is picked up. Through the choice relay the storage counter 70 24th column carry relay is picked up. If there is a 9 standing
in the 24th column of counter 70, the energized choice relay completes a circuit to pick up the storage counter invert relay.
Magnet
Seq-C-4-1,2
Seq-C-3-1,2,3
Seq-C-2-l,..,6
Choice Relay
SC70-11 24th Column Carry
Storage Counter Invert
Pick Up Circuit
FC-101 (3-2 1/3)
VBP-100
Seq-31-1,2,3,4
Reading Pins
FC-94
(12 1/2-13 2/3)
VBP-148
C-6-1-1 NC
C-5-1-1 NC
C-4-1-1
C-3-1-2
C-2-1-4
C-l-1-8 NC
Magnet
C-4-l-(12)
C-4-2-(6)
C-3-l,2,3-(12)
C-2-l,..,5-(12)
C-2-6-(6)
Choice Relay-(6)
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
C-4-2-6
C-3-3-11
C-2-6-6
SC-15
(13-15 1/3)
SBP-2-6
Choice-6
Cycle
Cycle 1
Circuit Diagram
+ FC-10 1 (3-2 1/3)
~^~FT.,_q,_ Seq-31-1
VBP^lOO
[Seq-31-2
lSeq-31-3
[Seq-31-4
( «-<*
C-4_
4-2-6
{ <-^
Q-r
fe-
C-2
*-o
FC-102 (4-9 3/4)
H
"7bF%2T~
■^SU
11
-Jb
J2-6-6
C-4-l-(12)
C-4-2-(6)
C-3-l,2,3-(12)
01 - F-18
C-2-6-(6)
+ . FC-94 (12 1/2-13 2/3)
""VBf£l48
FT. .qJ-6-l-i
c-4-1-1
1 _C-3 z l-2
♦C-2-1-4
t SC-15 (13-15 1/3)
SBP-23T
t c-i-^
Choice-6
_ -^F-14
hoice*
Relay-(6)
CHOICE COUNTER -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
FC-94
(12 1/2-13 2/3)
vbp-:l4Q
nc
C-6-1-1
C-5-1-1
C-4-1-1
C-3-1-2
C-2-1-4
C-l-1-8
Choice-6
Choice-1
9 Contact
SC-16
(14-15 1/3)
SBP-2-7
SC70--11-3
Choice-2
SBP-1-12
24th Column
Carry
SC70-ll-(4)
SC-15
(13-15 1/3)
SBP-2-6
Choice-1
+ FC-94 (12 1/2-13 2/3)
HI.- - .C-6-1-1
VBF^-148 f J3-5-1 -1
C-3-1-2
T C-2-1-4
c o-
«__£*«
SC-15 (13-15 1/3)
Choice-6
-O— - —
* ,Choice-l
Str Counter
Invert- (12)
SC--11 (12-0)
Invert-12
TT" o
-^—SBlfeo"-
+J3C-16 (14-15 1/3)
S 4 ' -45^00^(4)^
24th Col. Carry
10£
Choice-2
« o—
SC-11 (12-0)
IBL,
- F-14
Invert-12
Sj^^-r^v^rt^i^)
MIO CO UNTER ( Normal)
If the code Out 7321 or In 7321 is read by the sequence mechanism, the normal storage counter 71 out control or the normal storage counter
71 in control relay is energized. These in turn control the pick up of the normal storage counter 71 out and normal storage counter 71 in
relays respectively.
MJO CO UNTER ( Special)
CYCLE 0. Assuming that columns 13-24 of the MIO counter are to be read to columns 13-24 of register R, the sequence mechanism reads the
line of coding (853, R, blank). The sequence relays are energized. The special out (direct) relay is energized and through it the normal
storage counter out relays 2 and 3 are picked up. Assuming that columns 13-24 of the MIO counter are to be read to columns 1-12 of
register R, the sequence mechanism reads the line of coding (8531, R, blank). Through the corresponding sequence relays, the special out
(shifted) relay is energized and in turn the normal storage counter out relay 3 is picked up.
Assuming that columns 13-24 of register R are to be read into columns 13-24 of the MIO counter, the sequence mechanism reads the
line of coding (R, 853, blank) . The sequence relays are energized. The special in (direct) relay is energized and through it the normal
storage counter in relays 5 and 6 are picked up. Assuming that columns 1-12 of register R are to be read to columns 13-24 of the MIO
counter, the sequence mechanism reads the line of coding (R, 8531^ blank). Through the corresponding sequence relays, the special in
(shifted) relay is energized and in turn the normal storage counter in relay 6 is picked up.
CYCLE 1. If reading into the MIO counter, the carry control, carry, 24th column carry a,nd carry back control relays are energized. The
energized carry back control relay opens the carry circuit from column 12 to column 13 and closes an end around carry circuit from column
24 to column 13. The carry impulse may then complete the MIO counter entry.
MIO COUNTER -continued-
Magnet
Sequence relays
SC71-14 Normal Str Ctr Out Control
SC71-1,2,3 Normal Str Ctr Out
SC71-16 Normal Str Ctr In Control
SC71-4,5,6 Normal Str Ctr In
SC71-15 Special Out (direct)
SC71-18-1,2 Special Out (shifted)
SC71-17 Special In (direct)
SC71-19-1,2 Special In (shifted)
SC71-20 Carry Back Control
Storage Counter Magnets
Pick Dp Circuit
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1 NC
A-7-1-1
A-6-1-2 NC
A-5-1-3 NC
A-4-1-5 NC
A-3-1-9
A-2-2-6
A-l-3-12
SC-11 (12*0)
SBP-2-2
SC71-14-1
SC-11 (12-0)
SBP-2-2
SC71-14-2
SC71-15-1
SC-11 (12-0)
SBP-2-2
SC71-14-3
SC71-15-2
SC71-18-2-1
Magnet
Normal Str Ctr
Out Control
SC71-14-(6)
Normal Str Ctr
Out
SC71-1-(12)
Normal Str Ctr
Out
SC71-2-(12)
Normal Str Ctr
Out
SC71-3-(4)
Hold Circuit
SC-11 (12-0)
SBP-2-2
SC71-14-6
Cycle
Cycle 1
I I I I I I I I I
Circuit Diagram
FC-92 (12 1/2-13 2/3)
H T g A>8-l-l
VBftSSoT n A-7-l -l
F \A-4-l -5
Normal Out Control
SC71-14-(6)
I_^=2=l-9
SC-11 (12-0)
*—* — • — =o
* A=2 = 2-6
SBP-2-2
.SC71- 14-6
t qA-1--?-12
* f Ji ^at
+ . SC-11 (12-0)
H , ■ Q , SC71- 14-1 Normal Str Ctr Out
■sBp2 2 -2' t__ JL^-vvF-^
^^C7i^r-(i2)
+ SC-11 (12-0)
' H . r, _ r SC71- 14-2
aEPi53r T f" Normal Str Ctr Out
4- ,SC-11 (12-0)
1 H , _p . SC71- 14-3
Normal Str Ctr Out
SC71-3-(4)
- F-14
en
MIO COUNTER -continued-
Pick Up Circuit
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1 NC
B-7-1-1
B-6-1-2 NC
B-5-1-3 NC
B-4-1-5 NC
B-3-1-9
B-2-2-6
B-l-3-12
SC-11 (12-0)
SBP-2-2
SC71-16-1
SC-11 (12-0)
SBP-2-2
SC71-16-2
SC71-17-1
SC-11 (12-0)
SBP-2-2
SC71-16-3
SC71-17-2
SC71-19-2-1
FC-92
(12 1/2-13 2/3)
VBP-150
NC
NC
A-8-1-1
A-7-1-2
A-6-1-3
A-5-1-5
A-4-1-10 NC
A-3-2-7
A-2-4-2 NC
A-l-7-3 NC
Magnet
Normal Str Ctr
In Control
SC71-l6-(6)
Normal Str Ctr
In
SC71-4-(12)
Normal Str Ctr
In
SC71-5-(12)
Normal Str Ctr
In
SC71-6-(4)
Special Out
(direct-cols.
13-24 to cols.
13-24)
SC71-15-(6)
Hold Circuit
SC-11 (12-0)
SBP-2-2
SC71-16-6
SC-11 (12-0)
SBP-2-2
SC71-15-6
en
Circuit Diagram
+ £0=93 (12 1/2-13 2/3)
-EL^-oE^-i-l
VBliSw L_oB=2=l-l
4 ? B-6-l -2
f__cJk5=l-3
SQ=11 (12-0)
iQr-
■,SC71- l6-6
SBP-2-2
Normal In Control
SC71-l6-(6)
iL. -qB-3-1-9
t pB-2-2-6
t___oB=l=3-12:
J F-14
+ SC-11 (12-0)
_E[ ^_
n SC71-l6-l
SBP-2-2
Normal Str Ctr In
SC71-4-(l2)
JU-^J F-24
+ .SC-11 12-0)
-,. — r> — <?
SC71- 16-2
SBP-2-2
■f SC-11 (12-0)
■BL~-Q:
SBP-2-2
JSC71-16-3
JgC71rl7-2
JSC71-19-2-1
Normal Str Ctr In
SC71-5-02)
t F-14
Normal Str Ctr In
SC71-6-(4)
- F-14
+ FC-92 (12 1/2-13 2/3)
' H , Q A-8-l-l
vbKso - t
Special Out (direct)
SC71-15-(6)
SC-11 (12-0)
~H_* __q~
A-7-1-2
^l_oA-5 = l-5
i Ji-4-1-10
~f pA-g-2-7
t 0^=2-4-2
f pA-1-7-3
.SC71-15-6
t
SBP-2-2
T*-
F-14
MIO COUNTER -continued-
Pick Up Circuit
NC
NC
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1
A-7-1-2
A-6-1-3
A-5-1-5
A-4-1-10 NC
A-3-2-7
A-2-4-2 NC
A-l-7-3
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1
B-7-1-2 NC
B-6-1-3 NC
B-5-1-5
B-4-1-10 NC
B-3-2-7
B-2-4-2 NC
B-l-7-3 NC
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1
B-7-1-2
B-6-1-3
B-5-1-5
B-4-1-10 NC
B-3-2-7
B-2-4-2 NC
B-l-7-3
SC-13 (2-1 1/2)
Reset-10 NC
SBP-2-4
SC71-17-3
SC71-19-2-2
NC
NC
Magnet
Special Out
(shifted-cols.
13-24 to cols.
1-12)
SC71-18-1-(12)
SC71-18-2-(6)
Special In
(direct-cols.
13-24 to cols.
13-24)
SC71-17-(6)
Special In
(shifted-cols.
1-12 to oo Is.
13-24)
SC71-19-1-(12)
SC71-19-2-(6)
Carry Back
Control
SC71-20-(6)
Hold Circuit
SC-11 (12-0)
SBP-2-2
SC71-18-2-6
SC-11 (12-0)
SBP-2-2
SC71-17-6
SC-11 (12-0)
SBP-2-2
SC71-19-2-©
SC-14
(2-14 1/16)
SBP-2-5
SC71-20-6
Circuit Diagram
+ . FC-92 (12 1/2-13 2/3)
S.
VBPTISO T Q A-7-l -2
T A-6-1 -3 Special Out (shifted)
f A-5-1 -5 SC71-18-1-(12)
♦" .A-4-1 -10 SC71-18-2-(6)
^^-^1^=3=2-7
SC-11 (12-0)
SBP^2-2
SC71-18-2-6
* A-2-4-2
t ^
t — l ^W^ii^
+ FC-93 (12 1/2-13 2/3)
Special In (direct)
SC71-17-(6)
"—^ J ^B-6-1 -3
°~^ f _ B -5-l -5
° — T B-4-1-10
^^7_B-3-2-7
' ° 7 B-2-4-2
^SC-11 (12-0) T <£ — f B-l-7*3
* EZT wrt _i 7_A ' o x-
~5BF^2 ^~
+_ FC-93 (12 1/2-13 2/3)
' H . p B-8-l -l
SC71-17-6
^-jJ^T^lJ-*
SmpRi4T~r ^B-7-1-2
T_oB=6-l-3
J B-5-1-5
TB-4-1-10
' o
FB-3^2-7
Special In (shifted)
SC71-19-1-(12)
SC71-19-2-(6)
SC-11 (12-0)
7 B-2-4-2
X « _
SC71-19-2-6
T_B-l-7-3
t _
*— t ^W^—
+ SC-13 (2-1 1/2)
H . Reset -10
SC71-19-2-2'
SC-14 (2-14 1/16)
HFT . ~ ^SC71- 20-6
• SBP^ 3~^ — f
- F-14
Carry Back Control
SC71-20-(6)
CJI
MIO COUNTER -continued-
Pick Up Circuit
SC-10
(12-12 1/2)
SBP-2-1
Str Ctr Carry
Contacts
SC71-7,8-l,..,12
3071-11,10-1
SC71-20-1
Str Counter
Magnets
Hold Circuit
Circuit Diagram
+ , SC-10 (12-12 1/2) SC71-12-2
^o^ , ~jsC71-12-2
SBP=2^
S-l
9f
10f
1
. SC71-7-1
■jt ^
JQf
.29J
1
SC71-13-2
SC7W3--
SDH
9*~~
_T
a Carry Booster-12-(4)
^L- Coia
SC71-7-2
^Col.2
SC71-7-12
^Qy
SC?!- 1 ^^!
JPj
9£
10f
SC71-11-1
f
SC71 -10-1J
SC71-8-1
^L-
SC71-8-11
-JL
SC71-8-12
-JL-
Col. 12
q Carry Booster-13-(4)
Col. 13
Col. 23
Col. 24
- F-H
Str CtFiSgnets
AUTOMATI C CHECK COUNTER
CYCLE 0. Assuming that a positive tolerance is stored in switch R, the sequence mechanism reads the line of coding (R, 74, 7), and steps
to the next line. The corresponding sequence relays and through them the switch R out and storage counter 72 in relays are energized.
CYC1LE 1. The tolerance is read from switeh R into storage counter 72. Assuming that the quantity to be checked lies in storage counter
A, the sequence mechanism reads the line of coding (A, 74, 71), and steps to the next line. The corresponding sequence relays and through
them the storage counter A out relay, the aitorage counter 72 in relay and, if necessary to provide the negative absolute value, the stor-
age counter invert relay are energised.
CYCLE 2. The negative absolute value of the quantity standing in counter A is read into counter 72. The normal carry circuits are closed
and the carry impulse completes the entry. The sequence mechanism reads the line of coding (blank, blank, 64), and steps to the next line.
The corresponding sequence relays are energized and through them the check control relay is picked up. If the absolute value of the quan-
tity read in from counter A is less than the tolerance, the 24th column tens carry contact is made and the check relay is picked up.
CYC1LE 3. The energized check relay closeo a circuit shunted across the start relay points to pick up the read control
clutch magnet. Thus the oalculLator continues in operation only if the check relay is picked up.
relay and the
AUTOMATIC CHECK COUNTER -continued-
Magnet
Seq-C-6-1
Seq-C-4-1,2
Seq-8-1 Check Control
SC72-9 Str Ctr Carry Control
SC72-10 24th Column Carry
Check Relay
Seq-31-1 Read Control and Clutch Magnet
Pick Up Circuit
FC-101 (3-2 1/3)
VBP-100
Seq-31-1, 2,3, 4
Reading Pins
FC-96 (2-1 1/3)
VBP-172
C-6-1-2
C-5-1-2 NC
C-4-1-3
C-3-1-6 NC
C-2-1-11 NC
C-l-2-9 NC
SC-12 (11-14)
SBP-2-3
SC72-9-2
10 Contact
SC-12 (11-14)
SBP-2-3
SC72-10-2
Seq-8-1-1,2
Magnet
C-6-l-(6)
C-4-l-(12)
C-4-2-(6)
Check Control
Seq-8-l-(4)
Str Ctr 24th
Col. Carry
SC72-10-(4)
Check Relay-(4)
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
C-6-1-6
C-4-2-6
FC-102 (4-9 3/4)
VBP-225
Seq-8-1-3
SC-11 (12-0)
SBP-2-2
Check-4
Cycle 2
Cycle 3
Circuit Diagram
+.FC-1Q1 (3-2 1/3) pSsa^l-l
m
VBP-100
Seq-3 1-2
t
Seq-31-3
Sea=31-4
i FC-102 (4-9 3/4) t
■ H ... q. .
VBPi^25
+ FC-96 (2-1 1/3)
.C-6
.6-1-6
NiU
+*£=k-
4-2-6
t _
C-6-l-(6)
_ - F-18
C-4-l-(12)
C-4-2-(6)
'C-96 (2-:
"FT. q 02=6^1-2
VBP^7^° T_C-5-l-2
FC-102 (4-9 3/4)
H
set
VBP-225
+ , SC-1 2 (11-14)
sbp^t^
Seq-8 -1-3
Check Control
C-2-l -ll Seq-8-l-(4)
f p C-l-2 -9
T n .-.f-17
SC72-9-2
9t -
10f_
24th Column Carry
SC72-10-(4)
T F-14
+SC-12 (11-14)
H
"sbp^T
SC-11 (12-0)
Q SC72- 10-2 Seq-8 -1-1 ■ Check Relay-(4)
o§*£?-i-2 [ rJi^_r F -^
T— r
Check-4
AUTOMATIC CHECK COUNTER -continued-
Pick Up Circuit
FC-1C5 (4-2 1/2)
Sequence Cut-off
Svdtch
Card Feed #1 Sw.
Card Feed #2 Sw.
BBP-64
Check-1
BBP-54
FBP-9'8
Seq-32-1-1,2 NC
Magnet
Control Relay
Seq-31-.(4)
Hold Circuit
Circuit Diagram
+ FC-10 5 (4-2 1/2)
A s. /*
Seq.Sir. C.F.#1 Sw. C.F.#JTSw.
"BBP^oTT
.Check-1
~B*BP%4 FBP^8~
^Seq-32-1-1
^eq-32 -1-2
Read Control
Seq-31-l-(4)
- F-18
t
- F-19
Clutch Magnet
MULTIPLICATION CYCLE
To start multiplication, assuming the MC to lie in counter 8, code 4, the sequence mechanism reads the line of coding (4, 761, blank) . The
sequence relays are picked up. The multiply #1 and #2 relays are picked up. The sequence counter is advanced to read-out position 1. The
storage counter out and intermediate counter in relays are picked up. The DD-PQ reset relays are picked up.
Magnet
Seq-27 Repeat
Seq-33 Start
Seq-31 Control
Seq-A-4-1,2
Seq-B-7-1
Seq-B-6-1
Seq-B-l-l,..,ll
41 Multiply #1
38 Multiply #2
Sequence Counter Magnet
SC8-1,2,3 Storage Counter Out
50 Intermediate In
58 DD-PQ Reset
HD-6 DD-PQ Reset
Pick Dp Circuit
Seq-27-1
VBP-276
FC-103 (6-5 1/2)
VBP-277
Seq-27-2
FC-105 (4-2 1/2)
Sequence Cut-off
Switch
Card Feed #1 Sw.
Card Feed #2 Sw.
BBP-64
Seq-33-1
Seq-32-1,2 NC
FC-101 (3-2 1/2)
VBP-100
Seq-31-1, . . ,4
Reading Pins
Start
Seq-33-(4)
Control
Seq-31-(4)
Magnet
FC-108 (6-2 1/2)
VBP-278
Seq-33-4
Sequence
&-4-l-(12)
A-4-2-(6)
B-7-l-(4)
B-6-l-(4)
B-l-l,..,ll-(12) 3-1-11-11
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
fc-4-2-6
B-7-1-4
3-6-1-4
Circuit Diagram
+ Seq-2 7-1
<5 _JC-103 (6-5 1/2)
FC-10 8 (6-2 1/2)
C-103
VBP-276 " H , _ n Seq-27- 2
H
VBP^277
VBP-278
_<£e 3= 33-4
Start
Seq-33-(4)
+ T FC-10 5 (4-2 1/2)
__ _ _ _ o__ Seq-33- l
Seq.Sw. C.F.#1 Sw. C.F.#2 Sw. BBP:=6lrT'
-^F-18
Control
Seq-31-(4)
+ , FC-10 1 (3-2 1/2)
Vbp9[00
B-l-l,..,ll-(12)
MULTIPLICATION CYCLE -continued-
00
Pick Up Circuit
FC-95 (2-1 1/3)
VBP-171
B-8-1-2 NC
B-7-1-3
B-6-1-5
B-5-1-4 NC
B-4-1-7 NC
B-3-2-1 NC
B-2-3-1 NC
B-l-5-1
CC-49 (1-0 1/3)
41-2-5
Magnet
CC-10 (0-0 1/2)
38-3-3
14-1-3 NC
84-1-1 NC
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1
A-7-1-1
A-6--1-1
A-5-1-1
A-4-1-1
A-3-1-2
A-2-1-3
A-l-1-5
nc:
NC!
NC
NC
NC
NC
NC
Multiply #1
41-1,2-(12)
Multiply #2
38-l,2,3-(12)
Hold Circuit
48-1-1 NC or
CC-52 (1/3 3-16)
and
41-2-11
48-1-1 NC or
CC-52 (1/3 3-16)
and
38-3-11
Sequence Counter
Magnet
Storage Counter
#8 Out
SC8-1,2-(12)
SC8-3-U)
Circuit Diagram
SC-11 (12-0)
SC8-3-4
+ FC-95 (2-1 1/3)
3-8-1-2
48-1-1
CC-52 (1/3 3-16)
CC-52 (
— r~r ~
J3-7-1- 3
— r j-6-i- 5
— < ^~T J-5-1-4
T — &^ t b-4-1- 7
"^""f J-2-3-1
* f ^-l-5-l MD-37
* — f JU^
. Multiply #1
4^-2-11
41-1,2-(12)
+ CC-49 (1-0 1/3)
.48-1- 1
A n KD-37
CC-52 (i^l-161
TBL fe± n
Multiply #2
38-l,2,3-(12)
+ CC-10 (0-0 1/2)
-TBI
38-3-3
* — 4 J4-1- 3
*-TT 84-1-1
I o —
^— fi^&r 13
Sequence Counter Magnet
+ .FC-92 CL2 1/2-13 2/3)
_A -8-l-l
VBM50^~ T .A-7-1 -1
1 °^-T A-6-1-1
1 — ° :: -T A-5-1-1
l o a-4-1-1
T A -^
SC-ll (12-0)
^BL
SC8-3-4
7 .A-3-1 -2
° :; -T A-2-1-3
1 — ° — f _A-l-l -5 F-14
— ^ — X
Storage "Sounter Out
SC8-1,2-(12)
SC8-3-(4)
MULTIPLICATION CYCLE -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-1
41-1-1
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-1
41-1-2
CC-43 (12-0)
ABP-31-32-33
58-8-12
58-4-11,12
CC-62 (14-0)
Intermediate In
50-l,2,3-(12)
DD-PQ Reset
58-l,..,S-(12)
DD-PQ Reset
HD-6-(12)
CC-43 (12-0)
ABP-31-32-33
50-3-11
CC-43 (12-0)
ABP-31-32-33
58-8-12
58-4-11,12
4
— <j
±<
+
14-1-4
[ t , .CC-55 (12 1/2-13 2/3)
-1=1— — ,
O Q O O O 0,0 O O
112 3456789
Seq Ctr RO B-1
,0. ^-p-w
CC-43 (12-0)
_□ — . o — o — o
ABP-31-32-33
J4-1-4
t CC-57 (12 1/2-1
3 2/3)
0,0
5 6 7 8 9
R0 D-1
CC-62
o 50-3-ll
^-^^ Intermediate In
50-l,2,3-(12)
„ ^- md-39
J=L — *
O Q O O
1|2 3 4
Seq Ctr
CC-43 (12-0)
H "abp23£3£33
CC-43 (12-0)
M ■ O O o a 58 " 8 " 12
^^ DD-PCTReset
58-8-12 58-l,..,8-(12)
1 *
J58-4-II
J58-4-12
(14-0)
^- r D35^cTReset
HD-6-(12)
'ABp231-322 3 3f ♦
( 58-4-ll
J58-4-12
1 H .
CYCLE 1
The MC is read from storage to the intermediate counter. The intermediate counter carry control and carry relays are picked up and the
carry impulse completes the entry into the intermediate counter. The entry of a nine into the 24th column of the intermediate counter (a
negative MC) picks up the intermediate 24th column read-out control relay. The DD and PQ counters reset. The sequence counter is advanced
to read-out position 2. In preparation for the next cycle, the intermediate invert control and intermediate invert relays are picked up if
MC is negative. The "no shift" relays and MC-DR in relays are picked up in order to read the MC from the intermediate counter to the MC-DR
counters (l-2), (3-6), (5), (7) and (9). The entry control relays on MC-DR (1-2) and (3-6) prevent the multiple molding counters from short
circuiting the number impulses when the counters are in motion.
en
CO
MULTIPLICATION CYCLE 1 -continued-
Magnet
Pick Up Circuit
NC
SC-1,..,9
Str Ctr Reset
Stora,ge Ctr
Invert NC
Str Ctr BP
Str Ctr RO
SC8-1-1,..,
SC8-2-12
BBP-65,..,88
50-1-1,..,
50-2-12
CC-44 (2-1 1/3)
50-3-1
CC-45
(1/16. 11-13)
23-1-1
41 Multiply #1
38 Multiply #2
SC8-1,2,3 Storage Counter Out
50 Intermediate In
Intermediate Counter Magnets
23 Intermediate Carry Control
53 Intermediate Carry
89 Intermediate 24th column RO Control
58 DD-PQ Re»et
HD-6 DD-PQ Reset
PQ Counter Magnets
DD Counter Magnets
Sequence Counter Magnet
94 Intermediate Invert Control
HD-1 Intermediate Invert
43 MC-DR In
36 Shift.
91 MC-DR Entry Control (1-2)
92 MC-DR En try Control (3-6)
lllllllll
Magnet
Intermediate
Counter Magnets
Intermediate
Carry Control
23-1-U)
Intermediate
Carry
53-l,2-(12)
Hold Circuit
CC-46 (2-13 1/3)
ABP-35
23-1-4
OS
o
Circuit Diagram
+ SC-1,..,9
_o_c —
Str Ctr
Reset
T
Str Ctr 'str°Ctr BP
Invert
SC8-1-1, ,
d l o 2 3 o 4 ! J5 O 6 o 7 o 8 o 9° SC8-2-12
: q_
Str Ctr HO"
50-1-1, .
50-2-12
BBP-65,..,88 -(_.
Intermediate Counter Magnets
+ CC-44 (2-1 1/3)
CJC-46 (2-13 1/3)
3-35
[ritermediate
Carry Control
23-l--(4)
+ CC-45
(1/16 11-13)
23-1-1
J^ Intermediate Carry
53-l,2-(12)
MULTIPLICATION CYCLE 1 -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-12
(12-12 1/2)
Intermediate
Counter Carry
Contacts
53-1,2-12
Carry Booster
12-2,3
Carry Booster
13-2,3
24th col 3rd
mldg 9 spot
Intermediate
Counter
Intermediate
Counter
Magnets
Intermediate
24th col RO
Control
89-l-(4)
Intermediate
Carry Contacts
BB P-142 1
«f CC-12 (12-12 1/2) col. 1 9 » ° r
l Carry°BP |
col. 2 9*;
10J
col. 7 9*~
col. 8 9*~
col. 22 9*[
_ *3
col. 23 9£
, 10 T
col. 24 9*[
101
Intermediate
Carry Relay
_oS2=3=i
Jk±*
^3=1=7
Booster-12-2
j Booste r-12-3
jeet
^3-2-1
JtSd
11
%BP-140~*~
£:
BBP-144
53-2-1 2
t
Carry Booster-13 lies between columns 18 and 19.
+
BBP3L43
Intermediate
Counter Magnets
^iU
^SLs
■xS^
Carry Boost er-
12-(4)
- MD-7
-^
^ A >-s -.MD-1
~BBPil39 vii/ 5ol.24
col. 1
col. 2
col. 7
col. 8
col. 22
col. 23
o o o o o o o o o o
012345 6 78 9L O^-^vL^" -39
Intermediate Counter RO ^^^Intermediate 24th col RO Control
24th col 3rd mldg
89-l-(4)
MULTIPLICATION CYCLE 1 -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
to
CC-1,,.,9
HD-6-l,..,9
58-1-1,..,
58-4-10
PQ Counter
Magnets
CC-2 (2.-2 1/2)
^HI
CC-1 (1-1 1/2)
~HL
CC-3 (3-3 1/2)
~h:
CC-4 U-4 1/2)
"HI
CC-5 (5-5 1/2)
~HL
CC-6 (6-6 1/2)
^h.
CC-7 (7-7 1/2)
~.EL
CC-8 (8-8 1/2)
"HI
CC-9 (9-9 1/2)
~EL
PQ HO
HD-6-1 col.l
:;l-^i> t ,^-i-i coi.i
through
HD-6-2
L^o., -58-4-10 col.46
HD-6-3
*
HD-6-4
1 -A
-o— *(>-
HD-6-5
-o-^+o-
HD-6-6
~|HD-<
• o-
HD-6-7
o-
HD-6-8
-*- — o— *0-
HD-6-9
r~.i
-o-^O-J
to col.46 R0
PQ Counter
Magnets
Pick Up Circuit
CC-1,..,9
HD-6-l,..,9
58-5-1,..,
58-8-9
Magnet
DD Counter
Magnets
Hold Circuit
MULTIPLICATION CYCLE 1 -continued-
+.CC-1 (1-1 1/2)
I I t
CC-2 (2-2 1/2)
ti—
CC-3 (3-3 1/2)
ti-.
CC-5 (5-5 1/2)
H .
CC-4 (4-4 1/2)
t=L.
CC-6 (6-6 1/2)
CC-7 (7-7 1/2)
H .
CC-8 (8-8 1/2)
CC-9 (9-9 1/2)
Circuit Diagram
DD RO
HD-6 -1 col.1
-o— >■"• O-
. o ?8-5- l col. 1
through
HD-6-2
3 o_>2 qJ q58-8- 9 col.45
* . ^Jiri^ZJ^ 10
HD-6-3
-3
HD-6-4
. A J^ x JlD-9
HD-6-5
Jl_o_>5
o-
o-
o—
to col.45 RO
DD Counter
Magnets
1HD-6- 6
HD-6-7
o— ►" o-
-o— >' o-
HD-6- 8
-o— > O-h
HD-6-9
-o— >' o-J
OS
Pick Op Circuit
CC-10 (0-0 1/2)
38-3-3
14-1-3 NC
84-1-1 NC
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-2
CC-69
(15-16 1/3)
94-1-1,2
9 in 24th col
Intermediate
Counter
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-2
41-1-3
CC— "^3
(14-15 1/3)
43-2-12
35-45-1 NC
35-46-1 NC
Magnet
Sequence Counter
Magnet
Intermediate
Invert Control
94-l-(4)
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
94-1-4
Intermediate
Invert
HD-1-(12)
MC-DR In
43-l,..A0-(12)
43-ll,12-(4)
CC-43 (12-0)
ABP-31-32-33
HD-1-12
CC-43 (12--0)
ABP-31-32-33
43-10-12
43-12-3,4
Shift (No Shift)
36-37, 38~(12)
36-39-(4)
CC-43 (12-0)
AHP-31
36-39-2
MULTIPLICATIO N CYCLE 1 -continued-
2
Circuit Diagram
+ CC-10 (0-0 1/2)
"BL c3J=2=3
^£j>m
Sequence Count*
SequenceCounter Magnet
+,04-1-4
T CC-57 (12 1/2-13 2/3)
.O^OgO^O, 0,.0i0^0 d (>
CC-43 (12-0)
0"r2 Y3 o 4 o 5 o 6 o 7 o 8 Q 9° ^1-1-4
Seq Ctr RO D-2 »
ABPi31^32^33
+ CC-69 (15-16 1/3)
,94-1- 1 9 spot 4th mldg
24th column
,94-1- 2 | Intermediate Ctr
TT Q Q Q JTO-l- 12
ABP-31-32-33 i
j ^p 1 f CC-56 (12 1/2-13 2/3)
0°1°2^
_ -y4°5 6Ve 9° 41-l - 3
Seq Ctr RO C-2 {
0^3-10-12
43-fcr
L43-lV4
+ pC-33 (U-15 1/3)
~rTT ,43-2-12
- l - l ~* °^ ♦ 35-45- 1
X-4J (12-0) ^^^L_.<3J = 46-1
HR , Q J6-39-2 T_.
ABP-31 4>
_^ ^ MD-38
"intermediate Invert
Control 94-1- (4)
^MD-46
Intermediate Invert
HD-1-(12)
A _- MD-42
■^MT5-!t^.,lo-(i2)
_y^^MD-36
^ 43-ll-(4) MC-0R In
v MD-41
43-12-(4)
A __- MD-41
] v -*- / ~Shiffc 36-37,38 r (12)
36-39-(4)
MULTIPLICATION CYCLE 1 -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-76
(15-16 1/2)
43-12-1
43-12-2
MC-DR Entry
Control (1-2)
91-1,2,3-(12)
MC-DR Entry
Control (3-6)
92-l,2,3-(12)
CC-77 (16-0)
91-3-12
92-3-12
+ CC-76 (15-16 1/2)
4irl2-l
rJU
MC-DR Entry Control (1-2)
91-1,2,3-(12)
4 n W-.MD-32
'92-3-12 pMtC^DR Entry Control (3-6)
92-l,2,3-(12)
CYCLE 2
The sign control relays are picked up if the intermediate 24th column read-out control relay is up. The positive absolute value of the MC
reads from the intermediate counter to MC-DR counters (1-2), (3-6), (5), (7) and (9). The sequence counter advances to read-out position 3.
In preparation for the next cycle, the intermediate reset, first build-up, first and second build-up and the entry control relays for MC-DR
(3-6) and (4-8) are picked up.
Magnet
9 9
41 Multiply #1
38 Multiply #2
89 Intermediate 24th col RO Control
70 Sign Control #1
71 Sign Control #2
94 Intermediate Invert Control
HD-1 Intermediate Invert
43 MC-DR In
36 Shift
91 MC-DR Entry Control (1-2)
MC-DR Counter Magnets (1-2)
92 MC-DR Entry Control (3-6)
MC-DR Counter Magnets (3-6)
MC-DR Counter Magnets (5)
MC-DR Counter Magnets (7)
MC-DR Counter Magnets (9)
Sequence Counter Magnet
52 Intermediate Reset
HD-4 Intermediate Reset
44 First Build Up
45 First and Second Build Up
92 MC-DR Entry Control (3-6)
93 MC-DR Entry Control (4-8)
C
1
I
=
1
1
I
■
1
I
■
I
I
1
1
1
1
1
1
■
1
I
I
1
1
1
1
■
■
■
1
■
I
1
P
1
1
1
1
1
1
1
MULTIPLICATION CYCLE 2 -continued-
Pick Up Circuit
CC-9 (9-9 1/2)
43-6-'L2 or
39-3-2 or
57-3-2 and
89-1-1
Magnet
CC-7 (7-7 1/2)
43-11-4
70-1-2
CC-1,..,9
HD--1-1,..,10 NC
if MC was =•
HD-1"1,..,10 NO
if MC was <:
HD-4~1,..,9 NC
Intermediate RO
36-37-1,.. p
36-38-12
43-1-1,..,
43-2-11
I 43-3-1,..,
43-4-H
43-5-1,..,
43-6-11
43-7-1,..,
43-8-11
43-9-1,..,
43-10-H
CC-10 (0-0 1/2)
38-3-3
14-1-3 NC
84-1-1 NC
Sign Control #1
70-l-(4)
Hold Circuit
Sign Control #2
71-l-(4)
Counter Magnets
CC-75 (11-8)
BBP-145
or
BBP-60
52-3-6 NC
and
70-1-4
CC-74 (13 1/2-16)
or
47-13-1 NC
and
71-1-4
OS
OS
Circuit Diagram
±£G-9_(9-9 1/2)
or 13 9-3-2
, c q- 7 ,5 (H-8) p
^BI^^-^v-. or 157-3-2
BBPS45
+ CC-7 (7-7 1/2)
^BL. ^2rll-4
t o7Q-l-2
1 J^^O* fl5 -39
. J Sign Control #1
M^ 70-l-(4)
MC-DR (1-2)
MC-DR (3-6)
MC-DR (5)
MC-DR (7)
MC-DR (9)
Sequence Counter'
Magnet
CC-74 (13 1/2-16)
H . 072=1-4
<SL
-,MD-38
Sign Control #2
71-l-(4)
+ CC-1, ,.,9
""TT „ ^ii-i, . . ,10
E-oHD^l,..^
^o,o„o„o . o _o,o„o, 4 o„o
Qf )mm 'i r 7 m .'\
OT 2"3~4" 5 T6"7"8 V 9" ^ 6-38-12* ' 43-1-1, . . ,
Intermediate Ctr RO 4 ^3-2- 11
^-JJD-2
MC-DR Counter Magnets (1-2)
+ CC-10 (0-0 1/2)
~~J3L
38-3-3
84-1-1
T
^equ
13
"ounter Magnet
MULTIPLICATION CYCLE 2 -continued-
Pick Up Circuit
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-3
41-1-7
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-3
41-1-7
CC-61 (12-0)
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-3
41-1-5
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-3
41-1-6
CC-76
(15-16 1/2)
44-5-8
45-5-2
Magnet
Intermediate
Reset
52-l,2,3-(12)
Intermediate
Reset
HD-4-(12)
First Build Up
44-l,..,5-(12)
First and Second
Build Up
45-l,..,5-(12)
MC-DR Entry
Control (3-6)
92-l,2,3-(l2)
UC-DR Entry
Control (4-8)
93-l,2,3-(12)
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
52-3-11
CC-43 (12-0)
ABP-31-32-33
52-3-11
CC-61 (12-0)
CC-43 (12-0)
ABP-31-32-33
44-5-11
CC-43 (12-0)
ABP-31-32-33
45-5-11
CC-77 (16-0)
92-3-12
93-3-12
Circuit Diagram
+ 14-1- 4
"^^ T CC-57 (12 1/2-13 2/3)
o°iv 3 b
ABP-31232233
+ 14-1-4
F .CC-57 (12 1/2-13 2/3)
H
.0.0 _oo o.o.o^^o.o
pC-43 (12-0)
I I »
12 3 14 5 6 7 8 9
Sequence Ctr RO D-3
OzzChrzPz
ABPi^l^^ST
^2-3-1 1
+ 14-1-4
~° F , CC-55 (12 1/2-13 2/3)
0000
12 31
CC-A3 (12-0) Sequence Ctr RO B-3
4 5 6 7 8 9
EU
Px=0— O;
ABP-31-32-33
^044=5=11
+. 14-1-4
T ,00-56 (12 1/2-13 2/3)
~o,o_o_o
12 3 1 .
CC-43 (12-0) Seq Ctr RO C-3
o o„o o_o o
4 5 6 7 8 9
B1 is^i23^r- <fe5 lLL
+ CC-76 (15-16 1/2)
hb^.
<£fc£*
,o_o z o_o^o_o ., .
4 5 6 7 8 9 Q41-1- 7
CC-43 (12-0) Sequence Ctr RO D-3 t.
IT. ,0-0-0 52=2rll
- MD-43
Intermediate Reset
52-l,2,3-(l2)
^=k7
♦ 00-61 (12-0)
' H . .Q^V? MP-46
^ Jt ^ Intermediate Reset
HD-4-(12)
^1-1- 5
^-MD-42
FirsVBuild Up
44-l,..,5-(12)
, 41-1- 6
^^JrsVand Second Build Up
45-l,..,5-(12)
CC-77 (16-0)
45-5-2
,.92-3-12
t
+Sbi
MC-DR Entry Control (3-6)
92-l,2,3-(12)
4 I - 1 - MD-32
' J93-3- 12 N^^ECf-DR Entry Control (4-8)
93-l,2,3-(12)
a*.
-3
MULTIPLICATION CYCLE 3
The intermediate counter resets. Sign Control #1 drops out. If a nine stood in the 24th column of the intermediate counter a nine is read
to the 47th column of the PQ counter! The first build up takes place; i.e., twice the MC is read from the doubling moldings of MC-DR (1-2)
to MC-DR (3-6), (4-8), (5) and (9)„ The MC-DR carry control <ind carry relays are picked up and the carry impulse completes the first build
up. Assuming tne MP to 11. in storage counter 20, code 53, the sequence mechanism reads the line of coding (53, blank blank , ^ *he
sequence relAyt are picked up. The storage counter out and intermediate in relays are picked up i" order to read the MP to ^e intermediate
counter. The sequence counter i» advanced to read-out position 4. In preparation for the next cycle, the first and second build up,
second build up and the entry control r elays for MC-DR (4*8) are picked up.
OS
00
Magnet
41 Multiply #1
38 Multiply #2
52 Intermediate Reset
HD-4 Intermediate Reset
Intermediate Counter Magnets
70 Sign Control #1
71 Sign Control #2
PQ -47th column Counter Magnet
44 First Build Up
92 MC-DR Entry Control (3-6)
MC-DR Counter Magnets (3-6)
45 First and Second Build Ups
93 MC-DR Entry Control (4-8)
MC-DR Counter Magnets (4-8)
MC-DR Counter Magnets (5)
MC-DR Counter Magnets (9)
26 MC-DR Carry Control
49 MC-DR Carry
Seq-31 Control
Seq-A-5-1
Seq-A-3-1,2,3
SC20-1,2,3 Storage Counter Out
Sequence Counter Magnet
50 Intermediate In
45 First and. Second Build Ups
46 Second Build Up
93 MC-DR Entry Control (4-8)
I I
Pick Up Circuit
CC-9 (9-9 1/2)
82-1-9 NC
52-3-7
70-1-1
Magnet
PQ 47th column
Counter Magnet
Hold Circuit
I I
fi
Circuit Diagram
+ C C-9 (9-9 1/2)
.i~H « —
^82-1-9
T
.^2=1-7
4_
<Z2=]-1
JU— CJ *
■12
PQ 47th col Counter Magnet
MULTIPLICATION CYCLE 3_ -continued-
Pick Up Circuit
CC-1,..,9
HD-6-l,..,9
52-1-1,..,
52-2-11 and
52-3-5
Magnet
Intermediate
Counter Magnets
Hold Circuit
4 CC-1 (1-1 1/2)
CC-2 (2-2 1/2)
^b^ :
CC-3 (3-3 1/2)
HFT .
H_
CC-4 (4-4 1/2)
HL.
lCC-5 (5-5 1/2)
CC-6 (6-6 1/2)
ra^
CC-7 (7-7 1/2)
CC-8 (8-8 1/2)
CC-9 (9-9 1/2)
Circuit Diagram
Intermediate
Ctr RO
HD-4-1 col.l
r~L-^± o-j o52=lrl col. 1
4 H ^t__ ^J^
through
HD-4-2
-i o- 2 . o-
HD-4-3
^ o-2 0-4
HD-4-4
HD-4-5
-* o-^ o-+
" lHD-4 -6
o-# o~
HD-4-7
52-2- 11 col. 23
%o col. 23 ™ ^-*^l
RO
?2-3- 5 col. 24
v - MD-1
to BBP-141 and Intermediate
1 Q fr qI col. 24 RO Counter Magnets
-o-+ O-
HD-4-8
-* o-$ o-
HD-4 -9
J£ o-* CM
OS
CO
Pick Up Circuit
MC-DR Doubling
Read-out
91-3-1 on
columns 1-6
91-3-2 on
columns 7-12
etc.
MULTIPLICATION CYCLE 3 -continued-
Magnet
Hold Circuit
Circuit Diagram
91- 1-3
91-1-2
91-: .-1
Build Up RO
Reset RO
Impulses
_
.21=3-1,..,
91-3-5,..,"
—3°l-3-8
9
+b-j
Normal RO
— )►
Doubling RO
column 3
column 2
column 1
a*,
o
MULTIPLICATION CYCLE 3_ -continued-
Pick Up Circuit
CC-1,..,9
HD-2-l,..,10 NC
HD-5-l,..,9 NC
MC-DR (1-2)
Doubling RO
44-1-1,..,
44-2-12
44-3-1,..,
44-4-12
45-1-1,..,
45-2-12
45-3-1,..,
45-4-12
CC-44 (2-1 1/3)
45-5-1
CC-45
(1/16 11-13)
26-1-1
CC-12
(12-12 1/2)
Carry BP
Carry Transfer
Contacts
49-1,.., 10-12
MC-DR (3*6)
Carry Booster-1
MC-DR (4*8)
Carry Booster-2
MC-DR (5)
Carry Booster-3
MC-DR (7)
Carry Booster-4
MC-DR (9)
Carry Booster-5
Magnet
Hold Circuit
MC-DR Counter
Magnets (3-6)
MC-DR Counter
Magnets (9)
MC-DR Counter
Magnets (4-8)
MC-DR Counter
Magnets (5)
MC-DR Carry
Control
26-l-(4)
MC-DR Carry
49-l,..,10-(12)
MC-DR Counter
Magnets
CC-46 (2-13 1/2)
ABP-35
26-1-4
Circuit Diagram
+ . CC-1. ...9
"^=T. JID-2-l,..,10
T . pHD-5-l,..,9
12 3 4 J5 6 7 8 9
MC-DR (1-2) doubling RO
44-1-1,..,
MC-DR Counter
Magnets (3-6)
+ CC-44 (2-1 1/3)
CC-46 "(2-13 1/2 j
H
~ABf*$5~
. + CC-45 (1/16 11-13)
26-1-4 -
^-MD-35
J-DKCarry Control
l26-l-(4)
26-1-1
-^^mcCd>^" 43
Carry 49-l,..,10-(12)
+ CC-12 (12-12 1/2)
MC-DR Carry Conta cts (3-6) MC-D R Carry
9*"
col. 1 lOf
Carry BP
9*:
col. 2 io y
9£
col. 12 10 T
MC-DR Counter Magnets (3-6)
viL,
^2-lr2
-*JL
9i~
col. 23 lOy -
J&*d-
12
-JL
Booste r-l-2
Booster-1-3
j p-2- 3
Carry
Booster-l-(4)
9*
49-2-12
col. 24 10 V
t T
col. 1
col. 2
col. 12
^LA col.13
MULTIPLICATI ON CYCLE 3. -continued-
Pick Up Circuit
FC-105 (4-2 1/2)
Sequence Cut-off
Switch
Card Feed #1 Sw.
Card Feed 42 Sw.
BBP-64,110
44-5-1
BBP-111
FBP-133
216-1-2 NC
55-3-2 NC
78-2-8 NC
81-1-9 NC
BBP--52
FBP-99
201-1-2 NC
FBP-98
Seq-32-1,2 NC
FC-101 (3-2 1/2)
VBP-].00
Seq-31-1,.„,4
Reading Pins
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1 NC
A-7-1-1 NC
A-6-1-1 NC
A-5-1-1
A-4-1-2 NC
A-3-1-3
A-2-1-6 NC
A-l-1-11 NC
Magnet
Control Relay
Seq-31-(4)
Clutch Magnet
A-5-l-(12)
A-3-l,2,3-(12)
Storage Counter
#20 Out
SC20-1,2 -(12)
SC20-3-(4)
Hold Circuit
FC-102 (4-9 3/4)
VBP-225
A-fi-1-11
A-3-3-11
SC-11 (12-0)
SC20-3-4
Circuit Diagram
+ , FC-10 :> (4-2 1/2)
bl_x__:
eq.Sw. C.F.#1 Sw. C.F.#2 Sw.
^OrrOr
.44-5-1
BBP-64,110 *_
. ^216-1 -2
BBPilllFBP-133 f 5 5-3-2
-O — oi
L>2l=2-8
U
t__o8iar9
BBPi-52 FBP-9T T
3 Seq-3 2-l
PBP^f 2 " 21
^-pF-18
"Control Seq-31-(4)
-c F-19
^-^"clu^cli Magnet
+ FC-101 (3-2 1/2)
VBP-100
(fe^l-2 (
gea-21-3
A-5 o A-5-l-ll
,Seq-3 1-4
FC-102 (4-9 3/4)
hi:
Reading Pins
r^A- 5 -l-(12)
A-3
VBF^25"
J-FC-92 (12 1/2-13 2/3)
^wP2l5U° fA-7-l-i
A-3-3-11
A-3^,2,3-(12)
T -A-6-1 -1
TL_^=5=il-l
SC-11 (12-0)
J3C20-3-4
"°^T A-3-1 -3
~^~7 A-2-1-6
^A-l-1-11.
-J
to
}~f>^
Storage Counter Out
SC20-1,2-(12)
SC20-3-(4)
MULTIPLICATION CYCLE 3_ -continued-
Pick Up Circuit
CC-10 (0-0 1/2)
38-3-3
14-1-3 NC
84-1-1 NC
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-4
41-1-8
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-4
41-1-9
14-1-4 NC
CC-57
(12 1/2-13 2/3)
41-1-10
CC-76
(15-16 1/2)
45-5-2
Magnet
Sequence
Counter Magnet
Intermediate In
50-l,2,3-(12)
First and Second
Build Up
45-l,..,5-(12)
Second Build Up
46-l,..,5-(12)
MC-DR Entry
Control (4-8)
93-l,2,3-(12)
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
50-3-11
CC-43 (12-0)
ABP-31-32-33
45-5-11
CC-43 (12-0)
ABP-31-32-33
46-5-11
CC-77 (16-0)
93-3-12
Circuit Diagram
» CC-10 (0-0 1/2)
H , 3J = 3_-3
44-1-3
T 84-l- l
T K n ^-.MD-13
Sequence Counter Magnet
±<^el-4
T , CC-55 (12 1/2-13 2/3)
ai
o.o o o p o.o o
12 3 4 T5 6 7
CC-43 (12-0) Seq Ctr RO B-4
o o
8 9 41-1-8
ABP-31-32-33
q5Q-3-1 1
±^4r4
T , CC-56 (12 1/2-13 2/3)
o l o 2 o 3 O 4 ^5°6 o 7 O 8 o 9 O J J.-1-9
CC-4^3 (12-0) Seq Ctr RO C-4 *
:e
1bP^1?32^33
±<44=3-4
f CC-57 (12 1/2-13 2/3)
I I .
o^Vs ^Wsy ^1-1- 10
CC-43 (12-0) Seq Ctr RO D-4 £_
+ CC-76 (15-16 1/2)
~FT J.5-5- 2
cc-77 (16-0) T
^93-3-12
EC
^L-^-f^®" 32
jr MD-43
Intermediate In
50-l,2,3-(l2)
^>MD-42
First and Second Build Up
45—l,..,5-(12)
O^MD-42
Second Build Up
46-l,..,5-(12)
MC-DR Entry Control
93-l,2,3-(l2)
(4-8)
4^
-3
M ULTIPLICATION CYCLE 4
-a
4*-
The MP is read from storage to the intermediate counter as in cycle 1. The intermediate carry control and intermediate cany relays are
picked up and the carry impulse completes the entry into the intermediate counter as in cycle 1. The entry of a nine into the 24th column,
of the intermediate counter (a negative MP) picks up the intermediate 24th column read-out control relay as in cycle 1. The second build
up takes place; i.e., twice the MC is read from the doubling; moldings of MC-DR (1-2) to MC-DR (4-8) and (5) J six times the MG is read from
the doubling moldings of MC-DR (3-6) to MC-DR (7) and (9). The MC-DR carry control and carry relays are picked up and the carry impulse
completes the second build up as in cycle 3. The sequence counter is advanced to read-out position 5. In preparation for the next cycle
the intermediate invert control and intermediate invert relays are picked up if MP is negative. The MP in relay is picked up.
Magnet
41 Multiply #1
38 Multiply #2
SC20-1,2,3 Storage Counter Out
50 Intermediate In
Intermediate Counter Magnets
23 Intermediate Carry Control
53 Intermediate Carry
89 Intermediate 24th column RO Control
71 Sign Control #2
45 First and Second Build Up
93 MC-DR Entry Control (4-8)
MC-DR Counter Magnets (4-8)
MC-DR Counter Magnets (5)
46 Second Build Up
MC-DR Counter Magnets (7)
MC-DR Counter Magnets (9)
26 MC-DR Carry Control
49 MC-DR Carry
Sequence Counter Magnet
94 Intermediate Invert Control
HD-1 Intermediate Invert
39 MP In
Pick Up Circuit
CC-1,..,9
HD-2-l,,.,10NC
HD-5-l,..,9 NC
MC-DR (1-2)
doubling RO
45-1-1,..,
45-2-12
45-3-1,..,
45-4-12
46-1-1, . . ,
46-2-12
46-3-1, •«,
46-4-12
Magnet
MC-DR Counter
Magnets (4-8)
MC-DR Counter
Magnets (5)
MC-DR Counter
Magnets (7)
MC-DR Counter
Magnets (9)
Hold Circuit
I I
Circuit Diagram
+ CC-1. ...9
FT JjD-2-l,..,10
0°l o 2 o 3°4t
5°6 7 e 9°
45-1-1,..,
£5-2-1 2
MC-DR (1-2) doubling RO V A. ^-MD-4
MC-DR Counter
Magnets (4-8)
MULTIPLICATION CYCLE £ -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-10 (0-0 1/2)
38-3-3
14-1-3 NC
84-1-1 NC
14-1-4 NO
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-5
41-1-12
CC-69
(15-16 1/3)
94-1-1,2
9 in 24th col
Intermediate
Counter
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO C-5
41-1-11
Sequence Counter
Magnet
Intermediate
Invert Control
94-1- (4)
Intermediate
Invert
HD-1-(12)
MP In
39-l,2,3-(12)
CC-43 (12-0)
ABP-31-32-33
94-1-4
CC-43 (12-0)
ABP-31-32-33
HD-1-12
CC-43 (12-0)
ABP-31-32-33
39-3-11
+ CC-10 (0-0 1/2)
H , 38-3-3
t_^cl-3
T cA-i-l
1 , — ^SL~^9>- 13
Sequence Counter Magnet
+ 14-1-4
T , CC-57 (12 1/2-13 <
0°l o 2 o 3 O 4°5
CC-43 (12-0) Seq Ctr RC
!/3)
?6 7°8 o 9° .41-1-
>T5=5 **— f
c24=l:
t
-12
0-~r<Z, m ~3 e
+
H . o
ABP-31-32-33
CC-69 (15-16 1/3) -94-1-1
-4
Intermediate Invert
Control 94-l-(4)
H ♦
9 in 24th col
, ,94-1-2
CC-43 (12-0) t
H ~ « „ JffJ-1-12
- ±= 4bp%?32233^-L_
Intermediate CtrQ^^^.^-^MD-46
♦<
HD-1-(12)
,14-1-4
!/3)
?6 7°8 9° _41-1-
) C-5 ♦
T CC-55 (12 1/2-13 5
' H
0°l o 2 o 3 o 4°5
CC-43 (12-0) Seq Ctr RC
•11
"^^MPIn
39-l,2,3-(12)
J=L 1CBP%^255 ^~\
•11 '
CYCLE 5
Sign Control #1 is picked up if the intermediate 24th column read-out control relay is up as in cycle 2. The positive absolute value of the
MP reads from the intermediate counter to the MP counter and simultaneously the MP cycle control pick up relays, which are wired in parallel
with the MP counter magnets, are energized. The MP cycle control hold relays are set up by their pick up coils. The MP-DI7 control
relay is picked up. The sequence counter is advanced to read-out position 6, The intermediate reset relay is picked up. The cycle counter
is advanced to read-out position 1, The MP-DIV control hold relay is picked up preventing the sequence counter from advancing when CC-10
makes and further, preventing the passage of impulses from CC-55, 56 and 57 through the sequence counter read-out. The column shift left
and right relays are picked up. Impulses through the column shift left and right relays and the 2nd read-out molding of the MP counter
energize the required times left and right relays. If MP is zero, the C2, D2 and DD-PQ transfer #1 relays are picked up in place of the
column shift relays as in cycle 8 (5 + n).
-a
MULTIPLICATION CYCLE $ -eontinued-
OS
Magnet
Pick Up Circuit
HD-1«1,..,10 NC
HD-4-l,..,9 NC
Intel-mediate
Counter RO
39-1-1,..,
39-2-11
40-2-1 NC,.,.,
40-3-H NC
41 Multiply #1
38 Multiply #2
89 Intermediate 24th column RO Control
70 Sign Control ffl
71 Sign Control #2
94 Intermediate Invert Control
HD-1 Intermediate Invert
39 MP In
MP Counter Magnets
37 MP Cycle Control
13 MP-DIV Control Pick Up
Sequence Counter Magnet
52 Intermediate Reset
HD-4 Intermediate Reset
Cycle Counter Magnet
14 MP-DIV Control Hold
21 Column Shift Left
29 Column Shift Right
4 Times Left
5 Times Right
Magnet
MP Counter
Magnets
MP Cycle Control]
Pick Up
MP Cycle Control]
Hold
37-1,.., 26-
(4, 6 or 12)
■ rri
Hold Circuit
CC-41 (12-15)
ABP-34
or
BBP-133
30-1-1,2,8,9 NC
31-1-1,2,8,9 NC
and
37-2-3
37-4-3
37-5,.., 10-12
37-11,12-6
37-13,14-4
37-16-3
37-17,.., 22-12
37-23,24-6
37-25,26-4
Circuit Diagram
+ CC-1,
.,9
_ < £D = 1_-1 J ,..,10
^£=4-1,.. ,9
o l°2 o 3°4'
k£
C C-41 (12-15)
.a
o o o 39-1-1,..,
7 8°9 J9-2- 11 40-2-1, . . ,
Intermediate Ctr RO * , ^0-3- 11 MP Ctr Magnets
— =0z
bbp-:
133
ABP-34
£0-1-8,9
t
A31-1t1,2
c3M" 8 ' 9
N j L _^^JD-36
37-2-3
37-4-3
37-5,.., 10-12
37-11,12-6
37-13, 14-4
37-16-3
37-17,.., 22-12
37-23,24-6
37-25,26-4
MP Cycle Control
Pick Up
MP Cycle Control
Hold
37-l,..,26-(4,6 or 12)
MULTIPLICATION CYCLE £ -continued-
Pick Up Circuit
CC-26 (2-1 1/3)
39-2-12
CC-10 (0-0 1/2)
38-3-3
14-1-3 NC
84-1-1 NC
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-6
41-2-1
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-6
41-2-1
CC-61 (12-0)
CC-80
(1/16 12-9)
7-1,.., 9-2 NC
13-1-1
CC-54 (12*12 1/2)
Magnet
MP-DIV Control
Pick Up
13-l-(6)
Sequence
Counter Magnet
Intermediate
Reset
52-l,2,3-(12)
Intermediate
Reset
HD-4-(l2)
Cycle Counter
Magnet
CC-43 (12-0)
ABP-31-32-33
52-3-11
Hold Circuit
CC-47 (3 1/2-16)
13-1-6
CC-43 (12-0)
ABP-31-32-33
52-3-11
Circuit Diagram
+ CC-26
HI
(2-1
1/3)
CC-47 (3 1/2-16)
13-1-6
r-~ MD-34
'^^W-SlV Control Pick Up
13-l-(6)
+ CC-10 (0-0 1/2)
1 H . ,38-3- 3
♦ 14-l- 3
t_^l-l
Sequence Counter Ma
Magnet
+ JA-1- 4
t" CC-57 (12 1/2-13 2/3)
^ 3 — j
O l o 2 o 3 O 4 O 5 O 6 T7 O 8 o 9° J H-2-1
CC-43 (12-0) Seq Ctr RO D-6" °~~ f"
^52-3-H
H_
P^Oo^Os
ABP-31-32=33
+^-1- 4
f CC-57 (12 1/2-13 2/3)
j^ MD-43
"Intermediate Reset
52-l,2,3-(12)
CC-43 (12-0)
o l o 2 o 3 O 4 O 5°6 ?7 O 8 o 9 O ,41-2- 1
Seq Ctr RO D-6" £ CC-61 (12-0)
H^
AttQ^Q
ABP^3l^32=33
- MD-46
Intermediate Reset
HD-4-(12)
♦ t CC-80 (1/16 12-9)
:!C-a
-qj— lit • 1 9—2
f . 1 3 -1-1
♦ , CC-54 (12-12 1/2)
it
jr MD-13
Cycle Counter Magnet
-J
Pick Up Circuit
69-2-1,2 NC
13-1-3
CC-58
(14-15 1/3)
13-1-2
69-2-1,2 NC
13-1-3
CC-58
(14-15 1/3)
19-1-1 NC
18-1-1 NC
Cycle Ctr RO A-l
38— -1—1 , . . ,
38-2-1
37-1-1,..,
37-H-2
69-2-1,2 NC
14-1-1
CC-59
(14-15 1/3)
38-3-6
18-1-2 NC
Cycle Ctr RO C-l
38-2-2,..,
38-3-1
37-15-1,..,
37-26-2
CC-78 (15-16)
29-3n-5
MP Ctr RO
2nd mldg
(odd column)
MP-DIV Control
Hold
14-1-(12)
Magnet
Column Shift
Right
29-1,.., 36-
(12,12,6)
Column Shift
Left
21-1,.., 33-
(12,12,6)
Times Right
5-1,.., 27-
(12,12,4)
Hold Circuit
12-1,2-2 NC or
CC-32 (8 1/2-2)
and
L4-1-11
CC-36 (12-0)
&BP-27
29-3n-6
CC-36 (12-0)
ABP-27
!21-3n-6
CC-36 (12-0)
ABP-27
5-3n-4
MULTIPLICATION CYCLE i -continued-
-a
oo
Circuit Diagram
j. 69-2-1
to
~T _ J3--1-3
-g-2 f °-" T CC-58 (14-15 1/3)
, 112-2-2
CC-32 (8 l/2^2)t_
■^2-^ TT . i3-i-2
HL
.14-1-11
^ •- MD-34
-^^liP^DIV Control Hold
U-l-(12)
±i>9-2-l
£9-2-2
°~"T_CC-58 (U-15 1/3)
T | P , 18-1- 1
CC-36 (12-0)
m
ABP-27
^£2=221-6
38-1-1,..,
o l o 2 o 3 O 4° 5 f6 7°8 9° j ^ iw^T '
Cycle Ctr RO A-l f - MD-35
2-
Column Shift Right
29-l,..,36-(12,12,6)
±^2=2-1
,69-2-2
n
°~ 4 .C C-59 (14-15 1/3)
H . o38-?-6
t._JL8 = ^2
38-2-2,..,
CC-36 (12-0)
EL
_ _q p21-3 n -6
ABPi-27 4 ,
O l O 2 O 3 O 4 O 5 ?6 O 7°8 O 9 O ^ jfctt-2
Cycle Ctr RO C-l
8-3-1 37-15-1,..,
MD-35
1
Column Shift Left
21-1,..,33-(12,12,6)
+ CC-78 (15-16)
:C-78 <
CC-36 (12-0)
.<g2=3n^
o l o 2 o 3 O 4 O 5 O 6^7 O 8 o 9°
SBp227
MP Ctr RO 2nd mldg
<£2S-4
^MD-32
imes Right
5-l,..,27-(12,12,4)
MULTIPLICATION CYCLE j> -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-78 (15-16)
21-3n-5
MP Ctr RO
2nd mldg
(even column)
Times Left
4-1,.., 27-
(12,12,4)
CC-36 (12-0)
ABP-27
4-3n-4
+ CC-78 (15-16)
Times Left
4-l,..,27-(12 J
12,4)
H . o21-3n-5
oo ooo o,o co o
12 3 4 5 6T 7 8 9
CC-36 (12-0) MP Ctr RO 2nd mldg
H . 4-3n-4
ABP-27 ♦
CYCLE 6
The intermediate counter resets as in cycle 3. Sign Control #1 drops out. If a nine stood in the 24th column of the intermediate counter
a nine is read into the 47th column of the PQ counter as in cycle 3. The MC multiple selected by the times right relay is added into the
PQ counter. The PQ carry control and PQ carry relays are picked up and the carry impulse completes the entry into the PQ counter. The MC
multiple selected by the times left relay is added into the DD counter. The DD carry control and the DD carry relays are picked up and
the carry impulse completes the entry into the DD counter. The cycle counter is advanced. As in cycle 5 the column shift left and right
and times left and right relays are picked up. The MC multiples continue to be added in this manner in each successive cycle. When the
cycle counter reaches read-out position 9, the E relay is picked up. If MP was zero, this cycle (6) combines with cycle (6 + n) . The first
DD-PQ transfer takes place and the relays terminating the multiplication process are picked up as in cycle (6 + n). Here n indicates the
number of non-zero digits in the odd or even columns of the MP whichever is the greater.
Magnet
9 9
41 Multiply #1
38 Multiply #2
70 Sign Control #1
71 Sign Control #2
PQ 47th column Counter Magnet
52 Intermediate Reset
HD-4 Intermediate Reset
Intermediate Counter Magnets
37 MP Cycle Control
14 MP-DIV Control
21 Column Shift Left
29 Column Shift Right
4 Times Left
5 Times Right
PQ Counter Magnets
24 PQ Carry Control
62 PQ Carry
DD Counter Magnets
27 DD Carry Control
61 DD Carry
Cycle Counter Magnet
17 E
1
1
1
1
1
1
1
1
1 1
1 I
1
1
1
1
1
1
I*.
-a
to
MULTIPLICATIO N CYCLE 6 -continued-
Pick Up Circuit
Magnet
CC-1„..,9
HD-2«1,..,I0 NC
HD-5»1,..,9 NC
MC-DR RO
5-1-1,.., 5-26-12
3-19-1 NC,».,
3-20-12 nc
29— l—A, • • ,
29-36-12
56-3-1 NC,,.,
56-6-9 NC
CC-44 (2-1 1/3)
5-3n»l
38-3-7
CC-45
(1/16 11-13)
24-1-1
CC-1,..,9
HD-2-l,..,10 NC
HD-5-l,..,9 NC
MC-DR RO
4-1-1,.., 4-26-12
56-1-1 NC,..,
56-2-12 NC
21-1-1,..,
21-36-12
3-21-1 NC,..,
3-24-9 *£
CC-44(2-l 1/3)
4-3n-l
38-3-8
CC-45
(1/16 11-13)
27-1-1
PQ Counter
Magnets
PQ Carry Control
24-l-(4)
PQ Carry
62-i,..,4-(i2::
DD Counter
Magnets
Hold Circuit
CC-46 (2-13 1/3)
ABP-35
24-1-4
Circuit Diagram
DD Carry Control
27-1-U)
DD Carry
61-1,..,4-(12)
CC-46(2-13 1/3)
ABP-35
27-1-4
», C0i.. ., 1 9
"FT J?P-2-l,..,10
t .
)°l°2 3ti
MC-DR R(
O-O/O-OaO-0
5-1-1,..,
56-3-1,..,
6-6-9
**M$*&x
2°3t^O!rOl 5=26 r 12 3-19-1, . . ,
- PR RO ° ♦ . o 3-20-12 29-1-1,..,
, T . ogJ!=26-12
±ZJ
^MD-11,12
Counter Magnets
+ CC-44 (2-1 1/3)
j=T T , J-3n- l
c-&T2=IT5757
^8-3-7
^^-^ 4" 4 " ^^
- MD-35
Carry Control 24-l-(4)
+ CC-45 (1/16 11-13)
I I .
<2feJri
*&#**>*
Carry 62-l,..,4-(12)
+ CC-1. ...9
n=T T f fiD~2-1....10
T . qHD-5-1,..,9
oV2 ^ V6 7 8V 1:26- 12" 56-1-1,..,
MC-DR RO . 4 , ,56-2-1 2 21-1-1,..,
^n
r 3**2i—i, . * t
q ^ -i md«9,io
" A - ii> 'DD Counter Magnets
+ CC-44 (2-1 1/3)
y^A. 72-H W^ 1 ,38-3-8
'ABP%~ *~~7 ~^-~r-^DDCarry Control 27-1-U)
+ CC-45 (1/16 U-13)
£7-1-1
^^^MD-45
^DCarry 61-1, . . ,4-(12)
00
o
MULTIPLICATION CYCLE 6 -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-12
(12-12 1/2)
Carry BP
PQ Counter
Carry Contacts
62-1-1,..,
62-4-9
Carry Booster-
9-2,3
Carry Booster-
10-2,3
Carry Booster-
11-2,3
PQ Counter
Magnets
PQ Carry PQ Carry
4- CC-12 (12-12 1/2) Contacts Relay
"TBI.
Carry BP
col. 1 9£
lQf
PQ Counter
Magnets
col. 2 9*"
. lQf
.62-1-1
col.13 9£
1QJ
■JL
.62-1-12
col. 14 9£
10f
-JL-
.Booster-9-2
Booster-9-3
A62=2rl
^-^J®-"'
Carry Booster-9-(4)
col. 22 9£
~JL>
.62-2-9
10?
69-1-2
col. 1
col. 2
col.13
col. 14
-JJDrll
22
^&
t (*~&rr~T
Jt_« +, CC-2 g (3-14)
col. 23 9£
12?
H_
04-1-9
.62-2-10
col. 45 9£
m
-^ot 11
^2-4-8
col.46 9£
^su
JS2-4-9
23
col.45
hJID-12
46
^^sot:
Carry Booster-10 lies between columns 24 and 25.
Carry Booster-11 lies between columns 36 and 37.
oo
MULTIPLICATIO N CYCLE 6 -continued-
Pick Up Circuit
Magnet
Hold Circuit
CO
cc-12
(12-]L2 1/2)
Carry BP
DD Counter
Carry Contacts
61-1-1,..,
61-4-9
60-2,,.., 23-2 NC
Carry Booster-
6-2,3
Carry Boost, er-
7-2,3
Carry Booster-
8-2,3
DD Counter
Magnets
CC-80
(1/16 12-9)
7-1, ..,9-2 NC
14-1-5
CC-54 ,
(12-15 1/2}
Cycle Counter
Magnet
DD Carry
+ CC-12 (12-12 l/2)Contacts
^^col. 1 9*
DD Carry
Relay
.61-1-1
<£0=2>2
r , ^ col.22
col.23
col. 44
***>&- UD-iO
Carry Booster-7 lies between columns 24 and 25.
Carry Booster-8 lies between columns % > and 37.
+ CC-80 (1/16 12-9)
R T >l,-,9-2
o f JJ ^ J ^ 5
" ° * CC-54 (12-12 1/2)
_3,MD-13
3ycle Counter Magnet
MULTIPLICATION CYCLE 6 -continued-
Pick Up Circuit
69-2-1,2 NC
U-l-1
CC-58
(14-15 1/3)
19-1-1 NC
18-1-1 NC
Cycle Counter
Carry Contact
Magnet
E Relay
17-l-(4)
Hold Circuit
CC-36 (12-0)
ABP-27
17-1-4
Circuit Diagram
+<;£2=2rl
£2=2-:
2-JTT
=1-1
♦ . CC-5.8 (14-15 1/3)
19-1- 1
X_
w:
QC-36 (12-0)
gL
n 18-l- l
Cycle Ctr 9's
Carr y Contact
10 1
CYCLE 7 (4
T^th! 1 ? ^?^?^!^^ ad ? ed + i nto ^^ DD \ The appropriate column shift left and right and times left and right relays are picked up.
and n \Z Z,Z * + ? P ^ the P revi ? us SJ cl *> the P rela y * s «* Pi^ed up altering the read-outs of the cycle counter to read-outs B
and D. The cycle counter is advanced as in the previous cycle.
Pick Up Circuit
69-2-1,2 NC
14-1-1
CC-79 (6-5 1/2)
38-3-5
17-1-1
Magnet
41 Multiply #1
38 Multiply #2
71 Sign Control #2
37 MP Cycle Control
14 MP-DIV Control
21 Column Shift Left
29 Column Shift Right
4 Times Left
5 Times Right
PQ Counter Magnets
24 PQ Carry Control
62 PQ Carry
DD Counter Magnets
27 DD Carry Control
61 DD Carry
17 E
18 F
Cycle Counter Magnet
Magnet
F Relay
18-l-(4)
Hold Circuit
12-1,2-2 NC or
CC-32 (8 1/2-2)
and
18-1-4
Circuit Diagram
+#**
£2=2-2
14-1- 1
♦
■CC-79 (6-5 1/2)
J- J H.
.12-1-2
332=1-5
112-2- 2
t ol7-l-l
CC-32 (8 1/2-2)
J=d .
A&=±U
-JLA
F Relay
18-l-(4)
4*.
00
CO
MULTIPLICATION CYCLE 8 (5 + n)
The successive multiples of MC are added to DD and PQ. The: cycle counter is advanced,
used, the C2, D2 and DD-PQ transfer #3. relays are energized.
00
When all the significant figures in MP have been
Magnet
9
Pick Up Circuit
69-2-1,2 NC C2
14-1-1 66-l-(4)
CC-59 (14-15 1/3:
38-3-6
18-1-2 NC
Cycle Ctr RO
38-2-2,.., 38-3-1
37-26-2 NC
30-1-10 NC
69-2-1,2 NC D2
14-1-1 67-1-U)
CC-58 (14-15 1/3]
19-1-1 NC
18-1-1 NC
Cycle Ctr RO
38-1-1,.., 38-2-1
37-H-2 NC
31-1-10 NC
41 Multiply #1
38 Multiply #2
71 Sign Control #2
37 MP Cycle Control
14 MP-DIV Control
18 F
21 Column Shift Left
29 Column Shift Right
4 Times Left
5 Times Right
PQ Counter Magnets
24 PQ Carry Control
62 PQ Carry
DD Counter Magnets
27 DD Carry Control
61 DD Carry
Cycle Counter Magnet
66 C2
67 D2
74 DD-PQ Transfer #1
Magnet
69-1-3 NC or
CC-30 (1/16 3-1)
and
66-1-4
Hold Circuit
69-1-3 NC or
CC-30 (1/16 3-D
and
67-1-4
I I
I I
Circuit Diagram
+^5=1-1 U-4-X.J ^9 (14-1 5 1/3)
I olS-1- 2
<&2=lr3
cc-30 n7i6~3"aT
SL
o o o o o o,o_..
12 3 4 5 6 71
Cycle Counter RO
.o_o
38-2-2,..,
t__o32=26-2
^6-1-4
t
-c22=t 10
C2 66-l-(4)
~JLt*>J©-38
+ 69-2-1 14-1- 1 CC-5 8 (14-15 1/3)
~^T_^_J"~^^2=irl
39-2-2"?
cc-30 Tt/xTS-iT
0°l o 2 o 3 O 4°5
^
'sV
Cycle Counter RO
_o62=l-4
38-1-1,..,
<3J=2rl
^T 031-1- 10
D2 67-l-(4)
-MD-38
-~~SLj-&
Pick Up Circuit
CC-40
(1/16 15-9)
66-1-1
67-1-1
Magnet
DD-PQ
Transfer #1
74-l,2-(12)
74-3-(4)
MULTIPLICATION CYCLE 8 (5 + n) -continued-
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
74-3-4
Circuit Diagram
» t CC-4 p (1/16 15-9)
H
_66-l-l
pC-43
(12-0)
£t*rl
"AB?255?32%3
.74-3-4
vSbi
^jp-38
DD-PQ Transfer #1
74-l,2-(12)
74-3-(4)
CYCLE 2 (6 + n)
l^nllT ^L*™"?**, ta ^ 63 P ]T' ST* X "f ° f DD are added t0 columns 1 " 82 of «. The usual carry circuits are set up in the PQ
counter. The CD control relay picks up which permits the C and D relays to be energized. Picking up C and D drops out the MP cycle control
£" ™^-™ The r* CyCl * ? ounter n is a <*vanced ; The energized C and D relays permit DD-PQ transfer* #2, MP resefSK 2-DR reset to be Scked
Sines witf^lel 17 ** *" P UP# The Pi ° k UP ° f llWm reSet dropS ° ut ** contvo1 #2 ' * W ^3^^^ this cycle col-
Magnet
41 Multiply #1
38 Multiply #2
71 Sign Control #2
37 MP Cycle Control
14 MP-DIV Control
18 F
74 DD-PQ Transfer #1
PQ Counter Magnets
24 PQ Carry Control
62 PQ Carry
66 C2
67 D2
69 CD Control
30 C
31 D
Cycle Counter Magnet
59 DD-PQ Transfer #2
40 MP Reset
47 MC-DR Reset
HD-5 MC-DR Reset
91 MC-DR Entry Control (1-2)
92 MC-DR Entry Control (3-6)
93 MC-DR Entry Control (4-8)
Pick: Up Circuit
Magnet
CC-1,.., 9
HD-3-l,..,10 NC
HD-6-l,..,9 NC
DD Counter RO
74-1-1,..,.
74-2-10
CC-44 (2-1 1/3)
74-3-1
CC-26 (2-1 1/3)
74-2-11
CC-33
(14-15 1/3)
69-1-1
CC-40 (1/16 15-9!
30-1-3
31-1-3
PQ Counter
Magnets
PQ Carry
Control
24-1-U)
CD Control
69-l,2-(4)
MULTIPLICATION CYCLE £ (6 + n) -continued-
oo
en
Hold Circuit
CC-40 (1/16 15-9:
30-1-3
31-1-3
C Relay
30-l-(12)
D Relay
31-1-(12)
DD-PQ Transfer
#2
59-l,2-(12)
59-3-(6)
UP Reeet
40-l,2,3-(12)
CC-46 (2-13 1/2)
AHP-35
24-1-4
CC-47 (3 1/2-16)
69-1-4
CC-38 (11 1/2-9)
30-1-11
31-1-11
CC-43 (12-0)
ABP-31-32-33
59-3-6
CC-43 (12-0)
ABP-31-32-33
40-3-12
Circuit Diagram
+ CC-1,. ,9
.J=l_ o— r HD-6-l,..,9
,o_o.,o„o , o _o ,o o^o„o
O l O 2 o 3 O 4°5 Q 6 o 7T8T 74-2-l6"'
DD Counter RO + _ Q -.^~+r Jw-U., 12
^^ PQ Counter Magnets
+ CC-44 (2-1 1/3)
TSL ~o7A=!-l
CC-46 (2-13 1/2)
-_^-^"> MD **35
' <ii> l 5 Q&Irry Control
1lP%5~
.24-1-4
4__
24-l-(4
+ CC-26 (2-1 1/3)
VBL.
74-2-11
, CC-47 (3 1/2-16)
m
.69-1-4
+ CC-33 (14-15 1/3)
1S„. o^L-l
CC-38 (11 1/2-9)
n . -MD-40
l^cTcorltrol
69-l,2-(4)
"^|C Relay 30-l-(12)
^0-1- 311
~ "rr — MD— 35
pJ^JP^lTRriKr 31-1-(12)
+ CC-40 (1/16 15-9)
^ + -31-1-3
CC-43 (12-0) t n _-.MD-39
"- |_j' ' 39-3-6
+ CC-40 (1/16 15-9)
~ TTT ' , 30-1- 3
CC-43 (12-0)
TB01--32-33 ♦ .
■^TS5^f Transfer #2
59-l,2-(12)
59-3«(6)
,„ ,MD-37
UP Reaet
40-l,2,3-(12)
MULTIPLICATION CYCLE j (6 t n) -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-40 (1/16 15-S
30-1-3
31-1-3
U-2-4
9)MC
-DR Reset
47-l,..,13-(12)
CC-43 (12-0)
ABP-31-32-33
47-13-10,11,12
CC-40 (1/16 15-«
30-1-3
31-1-3
41-2-4
CC-63 (12-0)
9! MC
-DR Reset
HD-5-(12)
CC-43 (12-0)
ABP-31-32-33
47-13-10,11,12
CC-63 (12-0)
CC-76
(15-16 1/3)
47-13-2
47-13-3
47-13-4
MC-DR Entry
Control (1-2)
91-1,2,3-(12)
MC-DR Entry
Control (3-6)
92-l,2,3-(12)
MC-DR Entry
Control (4-8)
93-l,2,3-(12)
CC-77 (16-0)
91-3-12
92-3-12
93-3-12
+ . CC-40 (1/16 15-9)
H .
CC-43 (12-0)
o2°=L-3
H
.47-13 -10,11
abp^i^32^3T"^ r
.-2-4
, -41-2-
7l2~l
J^^-DlTReset
47-l,..,13-(12)
+ CC-40 (1/16 15-9)
30-1-3
Cg-4.3 (12-0)
JA-2-4
S
CC-63 (12-0)
<3 4^ = 13-10,11,12
ABP-31-32-33 t .
H
_ - MD-46
MC-DRReset
HD-5-(12)
+ CC-76 (15-16 1/3)
.47-13-2
CC-77 (16-0)
n=r .
' 91-3-12
,47-13-3
47-13-4
MC-DR Entry Control (1-2)
91-1,2,3-(12)
92-3-12
rJU
MC-DR Entry Control (3-6)
92-l,2,3-(l2)
,93-3- 12 l^Mff^Entry Control (4-8)
93-l,2,3-(12)
CYCLE 10 (7 + n)
The second DD to PQ transfer, adding columns 23-45 of DD to columns 23-45 of PQ takes place. The usual carry circuits are set up in the PQ
counter. The MC-DR, MP and cycle counters reset. The A relay is picked up, and the B relay also if PQ 47th column nines carry contact is
closed. Energizing of the A relay will cause the MP-DIV control relay to drop out and prevent further advance of the cycle counter. The
sequence counter advances to read-out position 7* In preparation for the next cycle, the product out and sequence counter reset relays are
picked up. If the B relay is energized, the PQ invert relay is picked up. Assuming the product is to be delivered to storage counter 40,
code 64, the sequence mechanism reads the line of coding (blank, 64, 7)» The sequence relays are picked up. The repeat relay and the
storage counter in relays are energized. •£
-a
MULTIPLICATION CYCLE 10 (7 + n) -continued-
Magnet
9 9
41 Multiply #1
38 Multiply #2
59 DD-PQ Transfer #2
PQ Counter Magnets
24 PQ Carry Control
62 PQ Carry
47 MC-DR Reset
HD-5 MC-DR Reset
91 MC-DR Entry Control (1-2)
MC-DR Counter Magnets (1-2)
92 MC-DR Entry Control (3-6)
MC-DR Counter Magnets (3-6)
93 MC-DR Entry Control (4-8)
MC-DR Counter Magnets (4-8)
MC-DR Counter Magnets (5)
MC-DR Counter Magnets (7)
MC-DR Counter Magnets (9)
40 MP Reset
MP Counter Magnets
14 MP-DIV Control
Cycle Counter Magnet
18 F
12 A
16 B
Sequence Counter Magnet
34 Product Out
48 Sequence Counter Reset
HD-3 DD-PQ Invert
Seq-31 Control
Seq-B-6-].
Seq-B-4-1,2
Seq-C-7-1
Seq-27 Repeat
SC40-4,5j6 Storage Counter In
i
1
III
1 I
I
1
■
■
i
i
1
1
1
1
1 1
■
I
■
1
1 1 1
III
II
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
::
::
1
1 1 1
1 1
1
i
■
i
1
1 1 1 1 1
1
■1
■1
1
I
i
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-1,..,9
HD-3-l,..,10 NC
HD-6-l,..,9 NC
DD Counter RO
59-1-1,.. t
59-2-11
PQ Counter
Magnets
+CC-1„...9
n=T , oHD-3-l,..,10
t . o« D -
6-1,.., 9
DD Counter RO
V
V
y
59-1-1,..,
^59-2-11
♦ i . a_ j _- MD-11,12
PQ"~Counter
Magnets
00
00
MULTIPLICATION CYCLE 10 (7 + n) -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-44 (2-1 1/3)
59-3-1
CC-1,..,9
HD-5-l,..,9
MC-DR RO
47-1-1,..,
47-12-12
CC-1,..,9
40-1-1,.., 9
MP Counter RO
40-2-1,..,
40-3-11
CC-1,..,9
Cycle Counter RO
59-3-3 or
47-2-12
69-2-1,2 NC
14-1-1
CC-60 (6-5 1/3)
59-3-2
69-2-1,2 NC
14-1-1
CC-60 (6-5 1/3)
59-3-2
PQ 47th column
9' 8 carry
contact
PQ Carry
Control
24-l-(4)
MC-DR Counter
Magnets
MP Counter
s
Cycle Counter
Magnet
A Relay
12-l,2-(4)
B Relay
16-1- (4)
CC-46 (2-13 1/3)
ABP-35
24-1-4
CC-29 (6-8)
12-1-4
CC-29 (6-8)
16-1-4
+ . CC-44 (2-1 1/3)
CC-46 (2-13 1/3)
Hp£3T~^
Ft. ^ .24-1- 4
^"^ PQ Carry Control
24-l-(4)
+CC-1, ..,9
TT. pHD-?-!,. -,9
t .
f> , o „o „o , p r O i O ,,0^0 «o
47-1-1,..,
0"l"2"3"4 r5"6"7"8"9" -47-12 -12
jsMD-2,,.,7
>DR Counter Magnets
+ CC-1. ...9
H . o4Q-i-i,..,9
PtO^O-,0, Oj-O^O-O-OrtO
40-2-1,..,
v r2"3"4"5"6"7t8^1_ o 40 = 2 = ll
MP Counter RO \
~ K *~ r ' MP~"Sounter Magnets
+ CC— 1, ..,9
47-2-12
o l o 2 y3 o 4 o 5 o 6 o 7 o 8°9° L>9-3V l
Cycle Counter RO-E + |
+^9=2-1
69-2-2
T5-8)
♦ , CC-60 (6-5 1/3)
H . 0*2=2=2
J^=lr4
Cycle Counter Magnet
f ^^^_ <= .MD-34,35
A Relay
12-1,2- (4)
+ ,69-2- 1
Q 62 = ?-2
L
?C-29" T6-8)
♦ CC-60 (6-5 1/3)
H=T , ^ 59-3-2 PQ 47th col.
—9l
t_
n - MD-34
loT t^nfRefay l6-l-(4)
MULTIPLICATION C YCLE K) (7 + n) -continued-
Pick Up Circuit
Magnet
Hold Circuit
CC-10 (0-0 1/2)
Sequence
38-3-3
Counter Magnet
14-1-3 NC
84-1-1 NC
14-1-4 NC
Product Out
CC-43 (12-0)
CC-57
34-3-(12)
ABP-31-32-33
(12 1/2-13 2/3)
34-3-12
Seq Ctr RO D-7
41-2-3
and
41-2-6
34-l,2-(l2)
CC-43 (12-0)
34-4-(4)
ABP-31-32-33
34-4-4
14-1-4 NC
Sequence
CC-43 (12-0)
CC-55
Counter Reset
ABP-31-32-33
(12 1/2-13 2/3)
48-l-(12)
48-1-6
Seq Ctr RO B-7
41-2-2
CC-40
DD-PQ Invert
CC-43 (12-0)
(1/16 15-9)
HD-3-(12) and
ABP-31-32-33
229-3-2 NC
HD-3-(4)wc
HD-3-12
16-1-1
FC-105 (4-2 1/2)
Control
Seq Cut-off Sw.
Seq-31-(4)
Card Feed #1 Sw.
Clutch Magnet
Card Feed #2 Sw.
BBP-64
12-1,2-3
55-3-2 NC
78-2:-8 NC
81-2-9 NC
BBP-52, FBP-99
201-1-2 NC
FBP-98
Seq-32-1,2 NC
O
Circuit Diagram
+ CC-10 (0-0 1/2)
"TBI o28=3_-3
^O-v-oMD-13
^Seqxienc
eqxience Counter Magnet
+ J.4-1- 4
~^T >C C-57 (12 1/2-13 2/3)
CC-43 (12-0) Seq Ctr RO D-7
JbzL-....^-£).
,41-2-3
Q^Ch
ABP^31-32-33
S&-6
< 3Jcl-12
Product Out
34-3-(12)
JS4"
34-4-(4)
iT^ -CC-55 (12 1/2-13 2/3)
_tZ3„_
CC-43 (12-0) O^VlVs^W h41-2-:
■1-6 f_
-2-2
^fflens^ ctr *° M ^
^.MD-42
Sequence Counter Reset
48-l-(12)
+ CC-40 (1/16 15-9)
IS
H
Tis^or
,229-3-2
■ffiF%I?3"2^3"
'tL^^l
o ^-zJ®-^
]°^T5!)-PQ Invert HD-3-(12), HD-3-(4)vc
+ FC-10 5 (4-2 1/2)
,12-1-3
SeqTSw" C.F.#I Sw. C.F.#2 Sw. BBP=64 + ^5-3- 2
^^_J ^T__o8i^:9
I 201-1-^2"
r^Cor&rol^ Seq-31-(4)
- F-18
__F-19
Clutch Magnet
MULTIPLICATION CYCLE 10 (7
f n
) -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
FC-101 (3-2 1/2)
B-6-l-(6)
B-4-l-(12)
B-4-2-(6)
C-7-l-(4)
Repeat Relay
Seq-27-(4)
Storage Counter
#40 In
SC40-4,5-(12)
SC40-6-(4)
FC-102 (4-9 3/4)
VBP-225
B-6-1-6
B-4-2-6
C-7-1-4
FC-107 (0-5 1/4)
VBP-280
Seq-27-4
SC-11 (12-0)
SC40-6-4
+ FC-101 (3-2 1/2)
VBP-100
1 1 . o f
Seq-31-l
i
. n ~
Seq-31-1„..,4
Vbp-ioo
♦
*&6
B-6-1-6
T
B-6-l-(6) ^
r>r /-17
Reading Pins
Seq-31-2
t
<
teq-31-3
t
( Seq-31-4
^4 ,
B-4-2-6
t
B-4-l-(12)^ ~
B-4-2-(6)
JWv-F-18
FC-102 (4-9 3/4)
t£7
b-7-1-4
i
C-7-l-(4) ~~
1
FC-107 (0-5 1/4)
VBP-280
4
VBP2225
FC-107 (0-5 1/4)
' H , r C-7-1-1
tepeat
eq-27-(4)
.-1
B-5-l-2
f B-4-1-3
° * B-3-l-6
t B-1-2-9
C-7-1-1
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1 NC
B-7-1-1 NC
B-6-1-1
B-5-1-2 NC
B-4-1-3
B-3-1-6 NC
B-2-1-11 NC
B-1-2-9 NC
VBP2280
♦
<
4 FC-93 (12 1/2-13
[ Seq-27-4
*-*■ — li
2/3)
^VB^9^
3C-11 (12-0)
-1-1
L_ol=7
.SC40
4
-1-1
' B-6-l
t
-6-4
Storage Counter In
SC40-4,5-(12)
SC40-6-(4)
CYCLE 11 (8 + n)
The product is read from the PQ counter to storage. The storage counter carry is completed. The sequence counter and the 47th column of
PQ counter are reset. The repeat relay permits the energizing of the start relay. The calculator continues in operation.
MULTIPLICATIO N CYCLE 11 (8 + n) -continued-
4*
to
Pick Up Circuit
NC
CC-1,..,9
HD-3-1, . •
HD-3-10
HD--6-l,..,9 NC
PQ Counter RO
Plug Wires
34-1-1,..,
34-2-11
Buss
SC40»4,5-(12)
CC~5 (5-5 1/2)
Seq Ctr HO
BBP-43
78-2-10 NC
83-1-4 NC
80-1-1 NC
BBP-44
FBP-176
238-1-2 NC
FBP-177
BBP-45
82-1-4
42-2-5
55-2-9
15-1-1
48-1-2
NC
NC
NC
NC
Magnet
34 Product Out
HD-3 DD-PQ Invert
SC40-4,5,<> Storage Counter In
Storage Counter Magnet
SC40-9 Storage Counter Carry Control
SC40-7,8 Storage Counter Carry
12 A
16 B
48 Sequence Counter Reset
Sequence Counter Magnet
PQ 47th column. Counter Magnet
Seq-27 Repeat
Seq-33 Start
Seq-31 Control
Seq Reslays
I I I I il I I
Magnet
Storage Counter
Magnet (cols.
1-23)
Sequence Counter
Magnet
Hold Circuit
Circuit Diagram
+ CC-1,.,,9
TT. -HD-3-1,.., 9
iHD-2-10
*_ ^
-0 K5 1°2°3^
°6 o 7 O 8 9°
Plug 34-1-1,..,
PQ Counter RO
4-2-11 SC40-4-1,..,
Wires » , p ,,3040=5-11
Buss t — vjL— ^-^l/-14
Storage Counter Magnet
Columns 1-23
+ CC-5 (5-5 1/2)
~^h:
O l O 2 Q 3 O 4 O 5 O 6° ^8 O 9 O Q ,78-2-10
Seq Ctr RO HbBP^43
^EL 8 ^" 1
BBP=44 FBP^76 t .
fbf57Tbijp^5 f > 2 - 2 - 5
f n 55-2-9
^^ ^8-1-2
Seq CtrTJagnet^
MULTIPLICATION CYCLE 11 (8 4 n) -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-9 (9-9 1/2)
HD-3-10
Col. 46 zero
Col .47 zero or 8
HD-3-11
Col. 47 9 spot
Plug Wires
34-2-12
Buss
SC40-5-12
Read 9 from 47th
col. of PQ to
24th col. of
storage counter
CC-2 (2-2 1/2)
71-1-3 NC
CC-1 (1-1 1/2)
71-1-2 NC
PQ 47th column
RO
134-3-9
Seq-27-1
VBP-276
FC-103 (6-5 1/2)
VBP-277
Seq-27-2
FC-105 (4-2 1/2)
Sequence Cut-off
Switch
Card Feed #1 Sw.
Card Feed #2 Sw.
BBP-64
Seq-33-1
Seq-32-1,2 NC
PQ 47th column
Counter Magnet
Start
Seq-33-(4)
Control
Seq-31-(4)
FC-108 (6-2 1/2)
VBP-278
Seq-33-4
4 CC-9 (9-9 1/2)
f t_ oS
.HJ^IO
2=6-1
col. 46
0"5 O l O 6 O 2 O 7 O 3 O 8°4 O l,
I
HD-3-11
& o o,o o o o & o o p l u 8 (34-2-12
col. 47 51627384 9
' 3 Wires
Storage Ctr Magnet
col. 24
Buss
^-^Q ^J- 3 *
4 CC-2 (2-2 1/2)
~TBL
71-1- 3
CC-1 (1-1 1/2)
H_
£1-1-2
0°5 o l o 6 o 2 o 7 o 3 o 8'
PQ 47th column RO
4 ^eq-2 7-1
"It" • FC-103 (6-5 1/2)
VbI%276- t-T ~ .Seq-2 7-2
FC-108 (6-2 1/2) VBP2277 ^*"_
S.
_<3A-2r9
^JL-^-O®-! 2
PQ 47th column
Counter Magnet
rs
VBP-278 r
Seq-33-(4)
4 FC-10 5 (4-2 1/2)
Seq.Sw. C.F.#1 Sw. C.F.#2 Sw. BBP^64
kg-32-1
^eq- 33-1 II
^F-18
Control
Seq-31-(4)
CO
RBAD-01 JT of Pg LOW-ORDER COLUMNS
CYCLE 11 (8 + n). Assuming that the low order columns of the product are to be delivered to storage counter 3, code 21, the sequence me-
chanism reads the line of coding (86, 21, 7)» The sequence relays are picked up. The special PQ out relay, the repeat relay and the
storage counter in relay are energized. If the B relay is energized, the special sign ralay and the DD-PQ invert relay are picked up,
CYCLE 12 (9 + n) . The storage coumter magnets are energized and the storage counter carry circuits completed. The repeat relay permits the
energizing of the start relay. The calculator continues in operation.
CO
jjagnet
Sequence Relays
100-1 Special Sign
99-1,2,3 Special PQ Out
HD-3, HD-3 wc DD-PQ Inve:rt
Storage Counter Magnets
Cycle 11
i
Cycle 12
Pick Up Circuit
NC
NC
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-L-1
A-7-1-2
A-6-1-3
A-5-1-6
A-4-1-H NC
A-3-2-9 NC
A-2-4-5 NC
A-l-7-9 NC
CC-40
(1/16 15-9)
229-3-2 NC
16-1-1
CC-33
(14-15 1/3)
99-3-1,2
100-1-1,2
CC-9 (9-9 1/2)
HD-3-I wc
99-2-12
Buss
SC3-5-12
Magnet
99-l,2-(12)
99-3-(4)
Special PQ Out
(col. 1-23)
100-1- (4)
Special Sign
HD-3-(12)
HD-3-(4) wc
DD-PQ Invert
Str Ctr Magnet
24th col.
Hold Circuit
CC-43 (12-0)
ABP--31-32-33
99-3-4
CC-47(3 1/2-16)
100-1-4
CC-43 (12-0)
ABP-31-32-33
HD-3-12
Circuit Diagram
^ C-92 (12 1/2-13 2/3)
VBP-350^ A-7-1 -S
l_oA=6jll-3
+ A-5-1-6 Special PQ Out (1-23)
T Jl-4-1-11 99-l,2-(12)
T . A-3-2 -9 99-3-(4)
^HF -A-2-4-5
CC-43 (12-0) f A-l-7-9 _MD-47
ABP231^2233 j _
.CC-40 (1/16 15-9)
I s *
krS r l3 i72^i"6T
229-3-2
- MD-47
DD-PQ Invert
- MD-46
HD-3-(12)
HD-3-(4) wc
t ^^52-5-12
Buss t.
Str Ctr Magnet
24th column
Pick Up Circuit
CC-1,..,9
HD-3-l,..,10 NC
HD-6-l,..,9 NC
PQ Ctr RO (1-23)
99-1-1,..,
99-2-11
SC3-4-1,..,
SC3-5-11
Magnet
Str Ctr Magnets
cols. 1-23
READ-OUT of PQ LOW-ORDER COLUMNS -continued-
Hold Circuit
,+ .cc-i,..,9
2=3.-1,.., 10
0°l o 2°3V5
PQ Ctr RO cols. 1-23
o,o o o o 99-1-1,..
i T6 7 8°9° .,99-2- 11
SC3-4-1,..,
* — ^>^b5-U
Buss t.
Str Ctr Magnets
cols. 1-23
NORMALIZING REGISTER
°™ 2: JSSkWSS&^iJWJ o 0<Ung <A ' 761 ' 7) * Md 8teps *° tho next llne - The "*"-*■*««• — *- - -j***
Magnet
Sequence Relays
101-1,2 Normalizing Register Read-in
102-1,.., 23 Digit Sensing
103-1,.., 23 Shift Positioning
Pick Up Circuit
FC-93
(12 1/2-13 2/3)
VBP-149
B-8-1-1
B-7-1-2 NC
B-6-1-3 NC
B-5-1-5 NC
B-4-1-9 NC
B-3-2-5
B-2-3-10
B-l-6-8
Magnet
101-1,2-(12)
Norm. Reg.
Read-in
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
101-2-12
Circuit Diagram
C=p (12 1/2-13 2/3)
VBlffiJT T -B-7-1 -:
.CC-43 (12-0)
PssOs^Cb
^ABP^l^^
T n B-6 -1 -3
I qB-^;1-5 Normalizing Register In
I B-4--l-9 101-1,2-(12)
f o B-2-3-10
001=2-12 t_^6- 8 MD-47
NORMALIZING REGISTER -continued-
Pick Up Circuit
SC-1,..,9
Str Ctr Reset NC
Str Counter
Invert-NC
Str Ctr BP
Str Ctr RO col.n
SCA-1-1,..,
SCA-2-11
Buss
101-1-1,..,
101-2-11
CC-37
(11-1/4 12)
102-23,.., 1-1
Magnet
102-1,.., 23-(4)
Digit Sensing
103-23,.., l-(4)
Hold Circui.t
CC-35 (9-12)
ABP-21
102~n-4
4:3-1-1 NC
or
CC-52(l/3 3-16)
and
103-23,.., 1-4
CO
OS
Circuit Diagrsim
-ElloSfcr ctr Reset
~\ eStr Ctr Invert
Digit Sensing
102-n«(4)
T . ^ . 102-n-(4)
StrCtr 1 SCA-1-1,.., 1 £ n £ 23
BP O l O 2 O 3 ?4 O 5 O 6°7 O 8 O 9%SCA-2-ll 101-1-1,..,
^
(9-12)
Storage Counter RO
column n
ABP-21
♦ CC- 37 (11-1/4 12) O 102-22=l
IL
.j^l-l
J.03-23-4
1
102-22-;
1103-22-4
t -
102-2-1
CC-52 (1/3 3-16)
^H
1-1-1
rSU
WhSrk
t
rSb-
£02=1-4
r&J
-0-oM=2-ll
Buss
<j,Q2-n-4
i ^QJ
jy MD-47
Shift Positioning
103-23,.. ,l-(4)
» MD-47
CYCLE 4. The power of ten selected by the digit sensing and shift positioning relays is read into the intermediate counter and into storage
counter E. The operations of multiplication cycle 4 are carried out. The sequence mechanism reads the line of coding (8321, C ; , 7), and
steps to the next line. The normalizing register read-out relay and storage counter C in relay are energized.
CYCLE 5. The operations of multiplication cycle 5 are completed. The amount of shift is read into storage counter C.
Magnet
9 Cycle 4 9
Cycle 5 9
103-1,.., 23 Shift Positioning
Intermediate Counter Magnet
104-1 Normalizing Register Read-Out
Storage Counter Magnets
_
1
B
1
1
1
I
1
I
1
1
1
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-1 (1-1 1/2)
46-5-2
103-(n)-l
Buss
50-1-1,., 50-2-12
Intermediate Ctr
Magnet
col.(24-n)
±JJfcl_(l-l
1,
(2
)
ij-2 50-1-1,.., Intermediate Ctr Magnet
♦ . ^03-(n)-l O 50-2~12 column (24-n)
f ^ T ♦ n^r MD-1
C . Q_„. 1 J. . O/./" — ^\-»
Buss
NORMALIZING REGISTER -continued-
Pick Up Circuit
FC-92
(12 1/2-13 2/3)
VBP-150
A-8-1-1
A-7-1-2 NC
A-6-1-3 NC
A-5-1-5 NC
A-4-1-9 NC
A-3-2-5
A-2-3-10
A-l-6-8
CC-1,..,9
103-n-2 or 3
104-1-1 or 2
Buss cols .20
and 21
Magnet
104-1-U)
Norm. Reg.
Read-out
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
104-1-4
Circuit Diagram
+ FC-92 (12 1/2-13 2/3)
"HE
, - n A-8-l -l
ygpffyT T ..a-7-1 -2
t A-5-1 -5 Normalizing Register Out
f a-4-1 -9 104-l-(4)
°^ T .A-2-3 -10
CC-43 (12-0) ° — T A-l-6-8 MD-47
1 O
+ CC-3 (3-3 1/2)
-H_
CC-2 (2-2 1/2)
"FT,
CC-1 (1-1 1/2)
^03-2 3-2
JL03-23-3
,3.03-2 2-3
103-22-2
103-21-2
J^U-3
-fe
103
103-13-3
-ter
103
103-12-3
-fer
103'
103-11-2
o
jL03-fcr"
^04-1-3
lOJcl-S
t—jSL^~^
Buss col. 20
Buss col. 21
CO
-3
NORMALIZING REGISTER -continued- oo
CYCLE 6. The operations of multiplication cycles 6 and 8 (5 + n) are carried out.
CYCLE 7. The operations of multiplication cycle 9 (6 + n) .ar« carried out. The sequence mechanism reads the line of coding (C, B, 32), and
steps to the next line. The sequence relays, storage counter C out relay, storage counter B in relay and the storage counter invert relay
are picked up.
CYCLE 13. The operations of multiplication cycle 10 (7 + n) are carried out. The nines complement of the amount of shift is read ^stor-
age counter C to storage counter B completing the computation of the exponent. The sequence mechanism reads the line of coding ^bianK,
blank, 7), and steps to the next line. The sequence relays are picked up.
CYCLE 9. Except for the pick up of the storage counter in relay, the operations of multiplication cycle 11 (8 + n) are ° a ^ ed fl °^« J|»
sequence mechanism reads the line of coding (86, D, 7), and steps to the next line. The sequence relays, the special PQ out relay and the
storage counter D in relay are energized.
CYCLE 10. The normalized quantity is read into storage counter D with its highest significant digit in the 23rd column. The repeat relay
permits the pick up of the start rtslay. The calculator continues in operation.
DIVISION CYCLE
To start division, assuming the DR to lie in counter 8, code 4, the sequence mechanism reads the line of coding (4, 76, blank) • As in multi-
plication cycle 0, the sequence relays are picked up. The divide relay is picked up. The sequence counter advances to read-out position 1.
The storage counter out relays are picked up as in multiplication cycle 0. The intermediate in and DD-PQ reset relays are picked up. The
heavy duty DD-PQ reset relay is energized as in multiplication cycle 0. _^_____
Magnet
Seq-27 Repeat
Seq-33 Start
Seq-31 Control
Seq-A-4-1,2
Seq-B-7-1
Seq-B-6-1
56 Divide
Sequence Counter Magnet
SC8-1,2,3 Storage Counter Out
50 Intermediate In
58 DD-PQ Reset
HD-6 DD-PQ Reset
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
FC-95 (2
VBP-171
B-8-1-2
B-7-1-3
B-6-1-5
B-5-1-4
B-4-1-7
B-3-2-1
B-2-3-1
B-l-5-1
BBP-103
-1 1/3)
NC
Divide
56-l,..,13-(12)
48-1-1 NC or
CC-52 (1/3 3-16)
and
CC-53 (11-16) or
BBP-91
FBP-140
199-1-1 NC
FBP-197
BBP-132
and
56-13-11
+ FC-95 (2-1 1/3)
TOP^7l f gB-7-1 -3
CC-52 (1/3 3-16]
3-5-1-4
~T pB-4-1-7
^T q B-3-2 -1
tLgddS- 1
n . 199-1 -1
BBP^91 FBP^54U F FBP-197 BBP- 132
CC-53 (11-16)
J6M3-U
BBP 103
^MD-44
Divide
'56-l,..,13-(12)
CC-10 (0-0 1/2)
56-13-1
14-1-3 NC
84-1-1 NC
Sequence Counter
Magnet
+ CC-10 (0-0 1/2)
tt ,
^6-13-1
J4-1-3
.84-1- 1
^"^ Sequence Counter Magnet
DIVISION CYCLE -continued-
Pick Up Circuit
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO 13-1
56-11-1
14-1-4 MS
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-l
56-11-2
CC-43 (12-0)
$8-8-]L2 •
58-4-U,12
CC-62 (14-0)
Magnet
Intermediate In
50-l,2 f 3-(12)
DD-PQ Reset
58-l,..,8-(12)
DD-PQ Reset
HD-6-(12)
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
50-3-11
CC-43 (12-0)
ABP-31-32-33
58-8-12
58-4-11,12
Circuit Dia.gram
±<44=lr4
k=lr4
^L- .CC-55 (12 1/2-13 2/3)
-hi—,
SC-43 (12-0)
B£J
0"l Y2 o 3 O 4 O 5 O 6 o 7 O 8 o 9° ^6-11 -1
Seq Ctr RO B-l t
'iM&rfZl&H
| f CC-57 (12 1/2-13 2/3)
I I
CC-43 (12-0)
.^O^rll
o l ?2 o 3°4 O 5 O 6 o 7 O 8 o 9 O
Seq Ctr RO D-l
W
aOzrOrrCfc
ABP-31-32-33
^8=8.-12
£8=4-11
+ .CC-43 (12-0)
^3,
o — o — o —
ABP^31%2=33
£B=8.-12
t_
g8-4-n
58-4-12
^8=1^12
.CC-62 (14-0)
HI,
Intermediate In
50-l,2,3-(12)
ivJL— C^D-39
^^DD-PQ Reset
58-l,..,8-(12)
_^^_^-^fD-46
^^DD-PQ Reset
HD-6-(12)
DIVISION CYCLE 1
The DR is read from storage to the intermediate counter. The entry of a nine into the 24th column of the intermediate counter (a negative
DR) picks up the intermediate 24th column read-out control relay. The DD, PQ and Q-shift counters reset. The sequence counter is advanced
to read-out position 2, In preparation for the next cycle the intermediate invert control and intermediate invert relays are picked up if
DR is negative. The shift pick up., shift and MC-DR in relays are picked up in order to read the DR from the intermediate counter to the
MC-DR counters with its first significant digit in the 23rd column of MC-DR (1-2). The entry control relays on MC-DR (1-2) and (3-6) are
energiised as in multiplication cycle 1.
DIVISION CYCLE 1 -continued-
Pick Up Circuit
CC-1,..,9
HD-6-l,..,9
Q-Shift RO
58-8-10,11
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-2
56-11-3
Intermediate Ctr
24th column
2nd mldg to
2nd mldgs O's
or
24th column
2nd mldg 9 to
3rd mldgs 9*s
Magnet
56 Divide
SC8-1,2,3 Storage Counter Out
50 Intermediate In
Intermediate Counter Magnets
89 Intermediate 24th column RO Control
58 DD-PQ Reset
HD-6 DD-PQ Reset
PQ Counter Magnets
DD Counter Magnets
Q-Shift Counter Magnets
Sequence Counter Magnet
22 Q-Shift Invert
94 Intermediate Invert Control
HD-1 Intermediate Invert
35 Shift Pick Up
36 Shift
43 MC-DR In
91 MC-DR Entry Control (1-2)
92 MC-DR, Entry Control Ci-(>S
Magnet
Q-Shift Ctr
Magnets
Shift Pick Up
35-l,..,46-(4)
Hold Circuit
CC-42
(12-1/3 16)
35-1,.., 46-4
I I
I I
■
...
■■■■Ill
Circuit Diagram
±^CC^..,9 < HD-6_-l,..,9
H . J ♦
o l o 2 o 3 o 4f5 O 6 o 7°8 o 9 o
Q-Shift Ctr RO
^Q^-
t Counter Magnets
+ 14 = L r 4
T ,00-55 (12 1/2-13 2/3)
SL
0°l°2t
3°4 5 6 7 8 9° ^56-11-3
Seq Ctr RO B-2
Intermediate Counter RO
col. 24 col. 23 col. 2 col. 1
2nd mol dings
CC-42 (12-1/3 16)
O
O Shift Pick Up Relays
O 3rd moldings 35-l,..,46-(4)
LJLJl
J35-46 -4
J35-4-4 [ ^5-2- 4
^ ^ *~^o
MD-
^40.
DIVISION CYCLE 1 -continued-
Pick Up Circuit
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-2
56-11-4
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-2
56-11--5
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-2
56-11-6
CC-33
34-15 1/3)
43-2-12
35-(2n + l)-l
35-(2n-l)-l NC
35-(2n)-l NC
Magnet
MC-DR In
43-l,..,10-(12)
43-H,12-(4)
Q-Shift Invert
22-l-(12)
Intermediate
Invert Control
94-1-U)
Shift
36-1,.., 39-
(4,6 or 12)
CJ1
8
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
43-30-12
43-32-3,4
CC-43 (12-0)
ABP-31-32-33
22-].-ll
CC-43 (12-0)
ABP-31-32-33
94-1-4
CC-43 (12-0)
ABP-31
36-1-4,..,
36-39-2
Circuit Diagram
±M=%±
.CC-56 (12 1/2-13 2/3)
C-56 {
^ 3°4 g 6 7 8 9° .016=31-4
CC-4 3 (12-0) Seq Ctr RO C-2 _ +„ ...j t^-t^^" ^
-O— — 0---0— —
JT .CC-56 (12 1/2-13 2/3)
i=L_ ..
,0 ? ,0 rOiO B O rt O n O
.<^=10-1!
k£=12-3
,14^=12-4
43-l,..,10-(12) UC-DR In
^"41-13^(4)
p C-43 (12-0)
1 2 < ?3 4 5 6 7 < W 3 6-11-5
Seq Ctr RO C-2 t - n - ^- .MD-35
g3J
+ J4-1-4
ABP^ 2 ?^
J!C-57 (12 1/2-13 2/3)
,. 22-1- 11
"^^^QTshm Invert
22-l-(12)
0V2 ?3 o 4 o 5°6 o 7 o e o 9 o , 56-11 -6
Seq Ctr RO D-2
4— ^O^-O^^
^"^ Intermediate Invert Control
- MD-41
36-3^,38,39-(12,12,4)
36-2-(6)
CC-43 (12-0)
FT ,, h
^^BP^l
•^6-1-4 ]^6-l-(4)
Shift
36-1,.., 39-( 4,6 or 12)
DIVISION CYCLE 2
The sign control relays are picked up if the intermediate 24th column read-out control relay is up as in multiplication cycle 2. The posi-
tive absolute value of DR reads from the intermediate counter to MC-DR counters (1-2), (3-6j, (5), (7) and (9). The positive absolute value
of DR is read through the shift relay so that its first significant digit lies in column 23 of MC-DR (1-2). The complement on nine of the
number of columns the DR is shifted left on reading into MC-DR (1-2) is read into the Q-shift counter. At carry time an elusive one is read
into the Q-shift counter. The sequence counter advances to read-out position 3. In preparation for the next cycle, the intermediate reset,
the first build-up and the first and second build-up relays are picked up. The entry control relays for MC-DR(3-6; and (4-8) are energized
as in multiplication cycle 2,
Magnet
9 09
56 Divide
89 Intermediate 24th column RO Control
70 Sign Control #1
71 Sign Control #2
94 Intermediate Invert Control
HD-1 Intermediate Invert
43 MC-DR In
36 Shift
91 MC-DR Entry Control (1-2)
MC-DR Counter Magnets (1-2)
92 MC-DR Entry Control (3-6)
MC-DR Counter Magnets (3-6)
MC-DR Counter Magnets (5)
MC-DR Counter Magnets (7)
MC-DR Counter Magnets (9)
22 Q-Shift Invert
87 Q-Shift "Elusive One" Control
88 Q-Shift "Elusive One"
Q-Shift Counter Magnets
Sequence Counter Magnet
44 First Build Up
45 First and Second Build Up
52 Intermediate Reset
HD-4 Intermediate Reset
92 MC-DR Entry Control (3-6)
93 MC-DR Entry Control (4-8)
c
■
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-10 (0-0 1/2)
56-13-1
14-1-3 NC
84-1-1 NC
Sequence Counter
Magnet
+ CC-10 (0-0 1/2)
H . o56-13-l
t c^-1-3
T dM" 1
t , ,0 . ^- MD-13
" s ^ Sequence Counter Magnet
Pick Up Circuit
CC-12
(12-12 1/2)
Carry BP
Q-Shift Ctr
Carry Contact
88-1-1,2
28-0.--1 NC
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-3
56-13.-7
14-1--4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-3
56-11,-8
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-3
56-11-9
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-3
56-13.-9
CC-61 (12-0)
Magnet
Q-Shift Ctr
Magnets
First Build Up
44-l,..,5-(12)
First and Second
Build Up
45-l,..,5-(12)
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
44--5-H
CC-43 (12-0)
ABP-31-32-33
45-5-11
Intermediate
Reset
52-l,2,3-(12)
Intermediate
Reset
HD-4-(12)
CC-43 (12-0)
ABP-31-32-33
52-3-11
CC-43 (12-0)
ABP-31-32-33
52-3-11
CC-61 (12-0)
DIVISION CYCLE 2 -continued-
o
Circuit Diagram
iCC-12 (12-12 1/2)
xd — ^ o~
"CarrylBP
Q-Shift 88-1-1
Carry Contact 1 4
col.l £8-1-1
9 r __. o^£_
col.l
2PT
^JU-
J*=kr
88-1-2
_o
4, col. 2 q I Magnets
3-13
5-STTift
Counter
4 14-1-4
~T CC-55 (12 1/2-13 2/3)
-3=L
0°1°2° 3 ?4 5 6 7 8 Q 9° 56-11-7
CC-43 (12-0) Seq Ctr RO B-3 ° £.
H ~ .44-5-11
"KB&Z&ygft
HrsVBuild Up
44-l,..,5-(12)
4 14-1-4
T CC-56 (12 1/2-13 2/3)
o l o 2 o 3 U o 5 o 6 o 7 o e o 9 o JS6-11-8
CC-43 (12-0) Seq Ctr RO C-3 ♦_ ^^-^J®' 1 * 2
~TT n 45-5-11 ~" P^^F&sTand Second Build Up
"abp25i5-J2%3 ° »
45-l,-.,5-(12)
4 14-1-4
~\ CC-57 (12 1/2-13 2/3)
o l o 2 o 3 ?4 o 5 o 6°7 o 8 o 9 c ' .56-11 -9
CC-43 (12-0) Seq Ctr RO D-3 "~° £
' S -™&&£nr- " 52 " 3 " n
.„. ^- .^D-A-3
' 0i " Intermediate Reset
52-l,2,3-(12)
+ 14-1-4
"T CC-57 (12 1/2-13 2/3)
o l o 2 o 3 ?4 o 5 o 6 o 7 o 8 o 9° 56^11-9
CC-43 (12-0) Seq Ctr RO D-3 °~~ ♦_ .CC-61 (12-0)
" Ig -^p%ig32%---^ T 11 ,
TZT n _- MD-46
.ntermediate Reset
HD-4-(12)
DIVISION CYCLE 2 -continued-
Pick Up Circuit
CC-1,..,9
HD-1-1,..,10 NC
if DR was >
HD-1-1,..,10 NO
if DR was <
HD-4-l,..,9 NC
Intermediate RO
36-1-1 or
36-2-1,2 or,..,
36-37-1,..,
36-38-11
43-1-1,..
43-2-11
43-3-1,...
43-4-11
43-5-1,
43-6-11"
43-7-1,.
43-8-11
43-9-1,
43-10-11
CC-1,..,9
22-1-1,.., 10
36-1-2,3 or,..,
36-35-11,12
CC-44 (2-1 1/3)
43-4-12
36-39*-l NC
CC-45
(1/16 11-13)
87-1-1
Magnet
Counter Magnets
MC-DR (1-2)
MC-DR (3-6)
MC-DR (5)
MC-DR (7)
MC-DR (9)
Q-Shift Ctr
Magnets
Q-Shift "Elusive
One" Control
87-l-(4)
Q-Shift
"Elusive One"
88-l-(4)
Hold Circuit
CC-46 (2-13 1/3)
ABP-35
87-1-4
Circuit Diagram
+ .cc-i,..,9
H . qHD=1,..,10
„o „ o „o „o a p o z o „ o rt o„o
36-20-1,..,
0"1"2"3"4 Y5 U 6"7"8"9" . 36-21-3 43-1-1, . . ,
Intermediate RO ♦ . q43-2- 11
t
+ CC-1, ..,9
22-1-1,. .,10
+ CC-44 (2-1 1/3)
TFT . 6 43-4- 12
CC-46 (2-13 1/3)
^=T . o rt 87-l- 4
- ABP ^5 ° ♦
+ CC-45 (1/16 11-13)
36=1.-2
£6-35-11
^36=35-12
t ^
^6=39-1
g7-l-l
MC-DR Counter Magnets
eol.l
col. 2
Q-Shift Counter Magnets
T^^^Q-Shift "Elusive One" Control
87-l-(4)
"^Q^ShSft "Elusive One"
88-l-(4)
o
DIVISI ON CYCLE 3 «
— • — — — - — — — «• <
<
As in multiplication cycle 3, the intermediate counter resets. If a nine stood in the 24th column of the intermediate counter, a nine is
read to the 47th column of the PQ counter as in multiplication cycle 3» The first build up takes place; i.e., twice the DR is read from
the doubling moldings of MC-DR (1-2) to MC-DR (3-6), (4-8), (5) and (9). The MC-DR carry control and carry relays are picked up and the
carry impulse completes the first build up. Assuming the DD to lie in storage counter 20, code 53, the sequence mechanism reads the line
of coiling (53, blank, blank). Th«s sequence relays and the storage counter out relays are picked up as in multiplication cycle 3 • The seq-
uence counter is advanced to read-out position 4. In preparation for the next cycle the intermediate in, first and second build up, second
build up and add-22 relays are enorgized. The entry control relays for MC-DR (4-8) are picke d up as in multiplic ation cycle 3»
Magnet
9 9
56 Divide
52 Intermediate Reset
HD-4 Intermediate Reset
Intermediate Counter Mapnets
70 Sign Control #1
71 Sign Control #2
PQ 47th column Counter Magnet.
44 First Build Up
92 MC-DR Entry Control (3-6)
MC-DR Counter Magnets (3-6)
45 First and Second Build Up
MC-DR Entry Control (4-8)
MC-DR Counter Magnets (4-8)
MC-DR Counter Magnets (5)
MC-DR Counter Magnets (9)
26 MC-DR Carry Control
49 MC-DR Carry
Seq-31 Control
Seq-A-5-I
Seq-A-3-1,2,3
SC20-1,2„3 Storage Counter Out
Sequence Counter Magnet
50 Intermediate In
45 First and Second Build Up
46 Second Build Up
93 MC-DR Entry Control (4-8)
32 Add 22
■
■
■
■
■
■ I
■
■
1
1
1
1
'
■
■
1
1
I
I
■
■
1
1
■
■
1
I
1
1
■
■
1
1
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-10 (0-0 1/2)
56-13-1
14-1-3 NC
84-1-1 NC
Sequence
Counter Magnet
+ CC-10 (0-0 1/2)
H . o56»l>l
t—oLki-3
T cA-
1-1
Sequenc
e
Counter Magnet
DIVISION CYCLE 3 -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-4
56-11-10
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-4
56-11-11
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-4
56-11-12
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-4
56-12-1
Intermediate In
50-l,2,3-(12)
First and Second
Build Up
45-l,..,5-(12)
Second Build Up
46-l,..,5-(12)
Add-22
32-l-(4)
CC-43 (12-0)
ABP-31-32-33
50-3-11
CC-43 (12-0)
ABP-31-32-33
45-5-11
CC-43 (12-0)
ABP-31-32-33
46-5-11
CC-43 (12-0)
ABP-31-32-33
32-1-4
+ JL4-1- 4
F CC-55 (12 1/2-13 2/3)
0°1° 2 3 4 ?5°6 7 8 9 ^ 6-11-10
pC , -4 ,3 (12-0) Seq Ctr RO B-4 ♦ . ft , ^-Jffl-43
1$&3&3£33
^0^11
Intermediate In
50-l,2,3-(12)
l^JUcl-4
F PC-56 (12 1/2-13 2/3)
■ H .
o l o 2 o 3 o 4 Y5°6 o 7 o 8 o 9 O ,56-11 -11
, CC-43 (12-0) Seq Ctr RO C-4 %_
^^^^3^ 33 ^' ^ ,
<_MD-42
First and Second Build Up
45-l,..,5-(12)
4 ^L4-l- 4
F .CC-57 (12 1/2-13 2/3)
o l o 2 o 3 o 4 ?5°6 o 7 o e o 9 o . 56-11-12
CC-43 (12-0) Seq Ctr RO D-4 ♦ , , ^^JD-42
" H . n r, n ^6-5- 11 Second Build Up
ABP^3l^32^3 ^* , I 46-l,..,5-(12)
+ ,44-1- 4
F .CC-57 (12 1/2-13 2/3)
o l o 2 o 3 o 4 ?5°6 o 7 o 8 o 9 o , 56-12 -1
, CCr4 3 (12-0) Seq Ctr RO D-4 ♦ , n ... ,~-ffD-35
H . r*—r> r> -3 2-1- 4 r" Add-22
ABP^3lS2^3
32-l-(4)
DIVISION CYCLE 4
The DD is read from storage to the intermediate counter as in cycle 1. The entry of a nine into the 24th column of the intermediate counter
(a negative DD) picks up the intermediate 24th column read-out control relay as in cycle 1. The second build up takes place as in multi-
plication cycle 4; i.e., twice the DR is read from the doubling moldings of MC-DR (1-2) to MC-DR (4-8) and (5); six times the DR is read
from the doubling moldings of MC-DR (3-6) to MC-DR (7) and (9) . The MC-DR carry control and carry relays are picked up and the carry im-
pulse completes the second build up as in multiplication cycle 3. From two dial switches, 22-N (where the operating decimal point lies be-
tween columns N and N + 1) is added into the Q-shift counter. The Q-shift carry control and carry relays are picked up and the carry im-cn
pulse completes the entry. The sequence counter is advanced to read-out position 5. In preparation for the next cycle, the intermediate®
DIVISION CTCIjS 4. -continued-
invert control and intermediate invert, relays (as in multiplication cycle 4) are picked up if DD is negative. The shift pick up, shift and
DD in relays are picked up in order to read DD from the Intermediate counter to the DD counter with its first significant digit in the 45th
column of DD.
01
o
oo
Pick Up Circuit
Magnet
56 Divide
SC20-1,2,3 Storage Counter Out
50 Intermediate In
Intermediate Counter Magnets
89 Intermediate 24th column RO Control
71 Sign Control #2
45 First and Second Build Up
93 MC-DR Entry Control (4-8)
MC-DR Counter Magnets (4-8)
MC-DR Counter Magnets (5)
46 Second Build Up
MC-DR Counter Magnets (7)
MC-DR Counter Magnets (9)
26 MC-DR Carry Control
49 MC-DR Carry
32 Add-22
Q-Shift Counter Magnets
25 Q-Shift Carry Control
28 Q-Shift Carry
Sequence Counter Magnet
94 Intermediate Invert Control
HD-1 Intermediate Invert
35 Shift Pick Up
57 DD in
36 Shift
Magnet
Hold Circuit
I I I 1 I I I
III
III
I I I I! ■ I
Circuit Diagram
CC-1,..,9
Add-22 Switches
86-1-1,2 NC
32-1-1,2
CC-44 (2-1 1/3)
32-1-3
Q-Shift Ctr
Magnets
Q-Shift Carry
Control
25-l-(4)
+ hCC=L..,9
Add-22
Switches
*£_
_<32=3e2
♦ .col. l
- MD-13
Q-Shift Counter Magnets
CC-46 (2-13 1/3)
ABP-35
25-1-4
+ CC-44 (2-1 1/3)
Tbp^55
^^_^^MD-35
Q-Shift Carry Control
25-l-(4)
DIVISION CYCLE 4. -continued-
Pick Up Circuit
CC-45
(1/16 11-13)
25-1-1
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-5
56-12-4
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-5
56-12-2
Intermediate
Counter
24th column
2nd mldg to
2nd mldgs O's
24th column
2nd mldg 9 to
3rd mldgs 9's
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-5
56-12-3
Magnet
Q-Shift Carry
28-l-(4)
Intermediate
Invert Control
94-l-(4)
Shift Pick Up
35-l,..,46-(4)
DD In
57-l,2,3-(12)
Hold Circuit
CC-43 (12-0)
ABP-31-32-33
94-1-4
CC-42
(12-1/3 16)
35-1,.., 46-4
CC-43 (12-0)
ABP-31-32-33
57-3-11
Circuit Diagram
+ CC-45 (1/16 11-13)
H
25-1-1
- MD-35
"*^""£shift Carry
28-l-(4)
+ 14-1- 4
"^ f i CC-57 (12 1/2-13 2/3)
I I
0° l 2 3 4°5 T6 7 8 9 J>6-12- 4
CC-43 (12-0) Seq Ctr R0T3^ 4
TZT
^
+ 14-1-4
"° f .CC-55 (12 1/2-13 2/3)
'JzU.
.94-1-4
t_
^HD-38
Ktermediate Invert Control
94-l-(4)
> l 2°3°4 5fe
Intermediate Counter RO
col. 24 col. 23 col. 2 col. 1
2nd moldings
Seq Ctr RO TRT
7°8°9° 56-12-2
CC-42 (12-1/3 16)
I I ,
fr 3^ ifr
o — o
o 45 r ___,
O 35-45-4] 35-3- 4 1 35-1- 4
o
o
O Shift Pick Up Relays
O 3rd moldings 35-1, . . ,46-(4)
— ° n t r
J35-46-4
il5=4r4
£5=2-4
^4 ^L ^
MD-
40
+ 14-1-4
"* f .CC-56 (12 1/2-13 2/3)
"*13_
0°l o 2 o 3 o 4° J '6 7 8 9° .56-12 -3
Seq Ctr R0^3 ° 7
CC-43 (12-0)
^» t jD .0 O 57-3-ll
57-l,2,3-(12)
01
o
CO
DIVISION CYCLE 4. -continued-
Pick Up Circuit
CC-33
(14-15 1/3)
57-2-12
35-(2n + l)-l
35-(2n-l)-l NC
35-(2n)-l NC
Shift
36-1,.., 39-
(4, 6 or 12)
Magnet
Held Circuit
CC-43 (12-0)
ABP-31
36-1-4,..,
36-39-2
Circuit Diagram
■i- CC-33 (14-15 1/3) 35-46
TFH T ? 57-2~12 35-4^ ^.X
-.MD-41
3^-37,38,39-(12,12,4)
36-2-(4)
36-l-(4)
Shift
36-l,..,39-(4,6 or 12)
DIVISION CYCLE 5
«5i«i control #1 is picked up if the immediate 24th column read-out control relay is up as in multiplication cycle 2. The poaitive abso-
lute value of the DD reads from the intermediate counter to the DD counter. The value of DD is read through the shift relay so that its
Srst fi^if ican? digits ?nto column 45 of the DD counter. The amount of the DD shift left is read into the Q-shift counter. The Q-
.Mf* J»™Z Moults are as in cycle 4. The sequence counter is advanced to read-out posdtion 6„ The intermediate reset relay is picked
fxp rSe MP-DIV ctntrX pick ^Sp S en! ^gizS. ^he cycle counter is advanced to read-out position l.The MP-DIV control hold re^y is picked
up'prlventing the sequence couSter frojAdvancing when CC-10 makes and further, preventing the passage of impulses from CC-55, 56 and 57
SrSS the^equence counter read-out. The compare control, compare in and colum n shift right r elays are picke d up.
Magnet
56 Divide
89 Intel-mediate 24th column RO Control
70 Sign Control #1
71 Sign Control #2
94 Intermediate Invert Control
HD-1 Intermediate Invert
36 Shift
57 DD In
DD Counter Magnets
Q-Sh:Lft Counter Magnets
25 Q-Sh:Lft Carry Control
28 Q-Sh:Lft Carry
Sequence Counter Magnet
52 Intermediate Reset
HD-4 Intermediate Reset
13 MP-D:[V Control Pick Up
Cycle Counter Magnet
8 Compare Control
14 MP-DIV Control Hold
3 Compare In
29 Column Shift Right
DIVISION CYCLE j> -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-1,..,9
HD-1-1,..,10 NC
if DD was >
HD-1-1,..,10 NO
if DD was <
HD-4-l,..,9 NC
Intermediate RO
36-1-1,..,
36-38-11
57-1-1,..,
57-2-11
CC-1,..,9
22-1-1,.., 10 NC
36-1-2,3 or„..,
36-35-11,12
(see Relay List)
CC-44 (2-1 1/3)
57-3-1
CC-45
(1/16 11-13)
25-1-1
14-1-4 NC
CC-57
(12 1/2-13 2/3)
Seq Ctr RO D-6
56-12-5
CC-26 (2-1 1/3)
57-3-4
DD Counter
Magnets
Q-Shift Counter
Magnets
Q-Shift Carry
Control
25-l-(4)
Q-Shift Carry
28-l-(4)
Intermediate
Reset
52-l,2,3-(12)
MP-DIV Control
Pick Up
13-l-(6)
CC-46
(2-13 1/3)
ABP-35
25-1-4
CC-43 (12-0)
ABP-3 1-32-33
52-3-11
CC-47 (3 1/2-16)
13-1-6
+ CC-1. ...9
H . Q HD-1-1,..,10
t ^D-4- l. . . ,9
o o o o O o,o o.o o
12 3 4 5 6 T7 8 9
Intermediate Ctr RO
36-1-1,..,
^6=18-11 57-1-1,
f , ^7-2-H
^Wcounter*
Magnets
+ CC-1, ..,9
TT , 22-1-1,..,10
36-1-2,3 or ,..
^6=21-11,12
^-*-^ Q-Shift Counter Magnets
+ CC-44 (2-1 1/3)
CC-46 (2-13 1/3) 4 ,
HH^ V ,25-1-4
-O 0=
ABP-35^
^-^- MD-35
°^Q-SKlft Carry Control
25-l-(4)
+ .CC-45 (1/16 11-13)
"^^^Q^Shift Carry
28-l-(4)
+14-1-4
"^ f CC-57 (12 1/2-13 2/3)
* ,H ,
o l o 2 o 3 o 4 O 5°6 f7 O 8 o 9 Q J S6-12-5
CC-43 (12-0) Seq Ctr RO D-5 °"
E
*ABP^3]^2233
4, CC-26 (2-1 1/3)
^FT . p 57-3 -4
^.MD-43
ntermediate Reset
52-1,2, 3-(12)
CC-47
(3 1/2-16)
^2=1-6
- MD-34
'^"mP^DTV Control Pick Up
13-l-(6)
DIVISION CYCLE 5 --continued-
Pick Up Circuit
CC-80
(1/16 12-9)
7-1,.. .,9-2 nc
13-1-1
CC-54
(12-12 1/2)
CC-80
(1/16 12-9)
7-1,.., 9-2 NC
13-1-1
69-2-1,2 NC
13-1-3
CC-58
(14-15 1/3)
13-1-2
CC-40
(1/16 15-9)
13-1-4
56-13-2
8-1-3,4
Magnet
Cycle Counter
Magnet
Compare Control
8-l-(4)
MP-DIV Control
Hold
14-1-(12)
69-2-1,2 NC
13-1-3
CC-58
(14-15 1/3)
19-1-1 NC
18-1-1 NC
Cycle Ctr RO A-l
56-9-1,..,
56-10-11-
Compare In
3-l,..,24-(12)
3-25-(4)
Column Shift
Right
29-34,35,36-
(12,12,6)
Hold Circuit
12-1,2-2 NC
or
CC-32 (8 1/2-2)
and
14-1-11
CC-39
(1/3 15-12)
3-24-11
3-25-1,2
IN9
Circuit Diagram
CC-36 (12-0)
ABP-27
29-36-6
+ CC-80 (1/16 12-9)
"^HI
7-1,.. ,9-2
T
13-1-1
"° — 7 CC-54 (12-12 1/2)
x TT _^-^MD~33
"* ^^^*Cycle Counter Magnet
+ CC-80 (1/16 12-9)
~EL £±,..,9-11
'""^'Compare Control
8-l-(4)
+,69-2-1
69-2=Z~T
0-
13-1-3
I L
CC-58 (14-15 1/3)
13-1-2
112-2-2
CC-32 (8 1/&STT
HBL _
t..
- MD-34
14-1-11
,JO *~SlP-BTV Control Hold
14-1-(12)
+ CC-40 (1/16 15-9)
~FT. Jl" 1 ^
CC-39 (1/3 15-12) £ .8-1-3
^-,MD-33
-1,..,24-(12) Compare In
- MD-38
-25-(4)
4 _69-2-l
>9-h
J69-
J
13-1-3
— o —
7 CC-58 (14-15 1/3)
FT.o 1 ^
CC-36 (12-0)
"ABP22T"
29-36-6
18-1-1
■°-T
0°1°2°3'
fifs fcyW 1 *
56-9-1,..,
6-10-11
Cycle Ctr RO A-l
Column
Shift Right
- MD-35
29*-34",35,36-
(12,12,6)
DIVISION CYCLE 6
The intermediate counter resets as in cycle 3. Sign control #1 drops out. If a nine stood in the 24th column of the intermediate counter
a nine is read into the 47th column of the PQ counter as in multiplication cycle 3. The DD and DR read into the DD and DR compare relays*
The comparison is made and the appropriate over-under relays picked up. The over -under relay permits the appropriate Q control relay to be
energized nhich picks up the proper times right relay. The column shift right and MC-DR invert relays are picked up in order to subtract
the DR multiple during the next cycle.
Magnet
9 9
56 Divide
70 Sign Control #1
71 Sign Control #2
PQ 47th column Counter Magnet
52 Intermediate Reset
HD-5 Intermediate Reset
Intermediate Counter Magnets
14 MP-DIV Control Hold
3 Compare In
29 Column Shift Right
6 DD Compare
2 DR Compare
1 Over-Under
7 Q Control
5 Times Right
29 Column Shift Right
HD-2 MC-DR Invert
n
1
E
1
■
I
1
■
I
1
|
Ej
I
■
1
■
■
I
1
M
■
■
■
■
■
■
■
■
■
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-1,..,9
HD-3-l,..,10 NC
HD-6-l,..,9 NC
DD RO
3-21-1,..,
3-24-9
56-3-1,..,
56-6-9
29-34-1,..,
29-35-11
3-19-1,..,
3-20-11
DD Compare
6-l,..,24-(12)
CC-28 (9-12)
ABP-24
6-1,.., 24-12
+ CC-1,..,9
H , HD-3-l,..,lC
I ■ c
HD-<
»
S-l,..,9
1 3-21-1,..,
o l o 2°3 o 4 o 5?6 o 7 o 8 o 9 o 3-24-9 56-3-1,..,
DD RO + ^6-6-9
29-34-1,..,
29-35-H 3-19-1,..,
CC-28 (9-12)
<H-
t
3-20-11
f
n _ - md-34
H 'Afepg24
p., ,24—12
t , rv
DD
6-:
Compare
L,..,24-(12)
DIVISION CYCLE 6 -continued-
Pick Up Circuit
CC-1 : ,..,9
HD-2«1,..,10 NC
HD-5-l,..,9NC
MC-DR RO
3-1-1,..,
3-18-12
CC-24 A,B,C,D
ABP-25,26
6-1,.., 24-
1, ..,9
2-1,.., 216-1 NC
2-1,.., 216-2
CC-37
(11-1/4 12)
3-24-10,12
1-1, .,.,432-1
Magnet
DR Compare
2-l,..,2l6-(4)
Over-Under
l-l,..,423-(4)
Q Control
7-l,..,9-(4)
Hold Circuit
CC-27 (9-12) *
ABP-23
2-1,.., 120-4
CC-28 (9-12)
ABP-24
2-"L21,.., 216-4
CC-34 (9-12)
ABP-20
1-1,.., 235-3
CC-35 (9-12)
ABP-21
1-236,.., 423-3
CC-38 (11 1/2-9)
7-1-3
Circuit Diagram
+ CC-1. ....9
"nr,^!,.. »iq
,HD-5- l,..,9
CC-27 (9-12)
ab^IF
fiq=^8 (9-12)
„o„o „o^o . o _o ,5 „o ^o„o
0"l o 2 o 3 u 4°5 o 6 Y7 u 8 o 9 u J ^lS-lT '
MC-DR RO t ^_
.QC-28 (
"L-^i,.., 120-4
,J^__^MD-14,..,22
^^DR Compare
2-l,..,2l6-(4)
ABP^24
2-121 ...'.2l6Jr 2-1, . . ,120~(4)
2-1^.., 216-1
+ CC-24 A,B,C,D 6-1... , 24-1,. .,9f ~ "T .. _
r~~i . r \ r \ - * 2— ]l, « • ,216— 2
abp^^t t , r ~ V .
(9-12)
cfckf»235-3
C-35 "(9-12)""ABP^0
ABP-21
Jd?26,.., 423-3
CC-37 (11-1/4 12)
3-24-10
1-46-1
-2/£l2'
XI&
CC-38 (11 1/2-9)
FT .,
J-l-3
-JL4
2-121,.., 216-(4)
-^T^Difbr 3 '- 31
^J^ l-(2n-l)-(4)
DD Under
l-(2n)-(4)
■^Jb
-+£j
l-l,..,235-(4)
1-236,.., 423-(4)
*
° T ■
1-44-1
1-43-1
^-.
1-2-1
.1-1-1
— O— — r-
^^TTcotI^i 4
^J 7-1-C4)
DIVISION CYCLE 6 -continued-
Pick Dp Circuit
CC-31 (12 1/2-9)
7-1,.., 9-1
69-2-1,2 NC
14-1-1
CC-58
(14-15 1/3)
19-1-1 NC
18-1-1 NC
Cycle Ctr RO A-l
56-9-1,..,
56-10-11
CC-40
(1/16 15-9)
14-1-2
56-13-2
8-1-3,4 NC
Magnet
Times Right
5-1,.., 27-
(12,12,4)
Column Shift
Right
29-34,35,36-
(12,12,6)
MC-DR Invert
HD-2-(12)
Hold Circuit
CC-36 (12-0)
ABP-27
5-3n-4
CC-36 (12-0)
ABP-27
29-36-6
CC-39
(1/3 15-12)
HD-2-(12)
Circuit Diagram
4 CC-31 (12 1/2-9)
FT , J-l t . .,9-l
CC-36 (12-0)
ABP^27
<J©-32
"TimesRight
5-l,..,27-(l2,12,4)
± < £9 = 2~1
6^2
^4=lrl
t . CC- 58 (14-15 1/3)
^FT , J-9-1- 1
SP-36 (12-0)
0°l o 2 o 3 o 4°5'
f6°7 c
ABP-27
_o22r26-6
n n n 56-9-1,..,
°8 9° , 56-10-11
Cycle Ctr RO A-l
S
+ CC-40 (1/16 15-9)
♦ 56-13-2
CC-39 (1/3 15-12)
n=r, j ro-2-i2
P^MC-DR Invert
HD-2-(12)
<J ffl) -35
Column Shift
Right
29-34,35,36
(12,12,6)
DIVISION CYCLB 7
The selected DR multiple is subtracted from DD (the elusive one substitutes for the end around carry) . The first digit of the quotient is
added into PQ. The cycle counter is advanced. The compare control, compare in and column shift left relays are picked up.
DIVISION C YCLE 2 -continued-
Magnet
Pick Up Circuit
CC-1,..,9
HD-2~1,..,10
HD-5-l,..,9 NC
MC-DR RO
5-n-l,..,
5-2n-12
3-19-1 NC,..,
3-20-12 NC
29-34-1,..,
29-35-12
56-3-1,..,
56-6-9
3-21-1 NC,..,
3-24-9 NC
CC-44 (2-1 1/3)
5-3n-l
56-13-4
CC-45
(1/16 11-13)
27-1-1
DD Counter
Magnets
56 Divide
71 Sign Control #2
14 MP-DIV Control Hold
HD-2 MC-DR Invert
5 Times Right
29 Column Shift Right
DD Counter Magnets
27 DD Carry Control
61 DD Carry
60 Elusive One
PQ Counter Magnets
8 Compare Control
Cycle Counter Magnet
3 Compare In
21 Column Shift Left
Magnet
DD Carry
Control
27-l-(4)
DD Carry
61-1,..,4-(12)
Hold Circuit
CC-46 (2-13 1/3)
AEP-35
27-1-4
Circuit Diagram
+ CC-1, ,.,9
"HH , cHP^-i, . . , 10
t Q HD-5- l,..,9
I •
0°l O 2 o 3 O 4°5 C
7°8°9°
5-n-l,..
,.5-2n.-12
MC-DR RO
3-19-1,.
J-20- 12
29-34-1,..,
J29-35-12
1
+ CC-44 (2-1 1/3)
1BL ^3nrl
CC-46 (2-13 1/3)
+ CC-45 (1/16 11-13)
t 56-13 -4
_27-l-4
56-3-1,..,
J56-6-9 3-21-1, ,
^.^.MD-35
DD Carry Control
27-1- (4)
DD-Counter
Magnets
-"MD-9,10
H^.
27-1-1
^^.-MD-45
__ Carry
61-1,..,4-(12)
DIVISION CYCLE 2 -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-44 (2-1 1/3)
5-3n-l
56-13-3
29-3n-l or
21-3n-l
CC-12
(12-12 1/2)
Carry BP
DD Carry-
Contacts
61-1-1,..,
61-4-9
60-1-1
60-2-1,2,.,
60-23-1,2
CC-1,..,9
5-3n-2
21-3n-2 or
29-3n-2
56-7-1,..,
56-8-11
Elusive One
60-l,..,23-(4)
CC-46 (2-13 1/3)
ABP-35
60-1,.., 23-4
DD Counter
Magnets
PQ Counter
Magnets
+ CC -4 4 (2-1 1/3)
^ TTT , ^ n-i
» , 36-13 -3 21-3n-l or
2P-46 (2-13 1/3) °f Q29-3H -1
TT . r > o 60-l» • . ,23-4 °^t .
+ CC-12 (12-12 1/2)
-H— = o=
CarryBP
-45
Elusive One
60-l,..,23-(4)
DD Carry-
Contacts
col. 1 9
10
JS1-1-1
col. 2 9
10
col. 22 9
10
col. 23 9
10
col. 24 9
10
col. 44 9
10
61-2-11
i d^ 1 - 2 -^
K 6l-4_-8
jl±*
» CC-1,. .,9
' H , 3 -30-2 21-3n-2 or
♦ Q 29-3n-2 56-7-1,..,
f~ .56-8- U
_60-2-2
_60-23-2
£-2
i.0-22-1
^0-23 -1
■^^reiu
- MD-12
Counter Magnets
DD Counter
Magnets
« c- *- °
jso-fcn ^H coi. i
l 61-1-2 t
1 (61-2-10 tl
■^SL-
-JL/
col. 2
col. 22
col. 23
1 JLi - M> -9
col.24
■*JU
col.44
^u-sU^ 10
col«45
Pick Up Circuit
CC-80
(1/16 12-9)
7-1,.., 9-2 NC
14-1-5
CC-40
(1/16 15-9)
14-1-2
56-13-2
8-1-3,4
69-2-1,2 NC
14-1-1
CC-58
(14-15 1/3)
19-1-1 NC
18-1-1 NC
Cycle Ctr RO A-2
56-9-1,..,
56-10-12
Magnet
Compare Control
8-l-(4)
Compare In
3-l,..,24-(12)
3-25-(4)
Column Shift
Left
21-31,32,33-
(12,12,6)
Hold Circuit
CC-39
(1/3 15-12.)
3-24-H
3-25-1,2
CC-36 (12-0)
ABP-27
21-33-6
DIVISION C YCLE 7. -continued-
Circuit Diagram
hl.CjC-80 (1/16 12-9)
CjC-80 i
.... — cJfcJ jj • , '
9-2
_oX4=lr5
t__ „4L— ^c 1 ®- 34
Compare Control
8-l-(4)
(1/16 15-9)
±^2=2-1
tM-l-l
t .CC-58 (14-15 1/3)
3.MD-33
Compare In
3-l,..,24-(12)
3-25-(4)
CC-36 (12-0)
I I » rv—
ABP-27
^1=23-6
o l o 2 c, 3°4 o
Cycle Ctr RO A-2
3
/0_0-0_Q
6 7 8 9
56-9-1,..,
_j>6-10-12
t—p^JU-
- MD-35
Column Shift Left
21-31,32,33-(12,12,6)
DIVISI ON CYCLE 8
This cycle duplicates the compare) operations of cycle 6. During the latter part of the cycle, column shift left and times right relays are
picked up in preparation for the next cycle.
DIVISION CYCLE 8 -continued-
Magnet
9 9
56 Divide
71 Sign Control #2
14 MP-DIV Control Hold
3 Compare In
21 Column Shift Left
6 DD Compare
2 DR Compare
1 Over Under
7 Q Control
5 Times Right
21 Column Shift Left
HD-2 MC-DR Invert
EEEE
1
EEE
1
E
§
1
■
E
1
■
1
M
■
g
g
■
M
1
■
■
H
DIVISION CYCLE 9
This cycle duplicates the subtract operations of cycle 7 and the entry into the PQ counter, except for the interchange of right and left on
the column shift relays.
Magnet
9 9
56 Divide
71 Sign Control #2
14 MP-DIV Control Hold
HD-2 MC-DR Invert
5 Times Right
21 Column Shift Left
DD Counter Magnets
27 DD Carry Control
61 DD Carry
60 Elusive One
PQ Counter Magnets
Cycle Counter Magnet
8 Compare Control
3 Compare In
29 Column Shift Right
1
1
I
I
1
I
■
I
1
I
1
■
1
I
1
I
1
1
1
■
1
DIVISION CYCLE 10
The alternate compare and subtract cycles continue as in cycles 8 and 9. When the cycle counter reaches read-out position 9, the E relay is
picked up*
CD
DIVISION CYCLE 10 -continued-
o
Magnet
56 Divide
71 Sign Control #2
14 MP-DIV Control Hold
3 Compare In
29 Column Shift Right
6 DD Compare
2 DR Compare
1 Over-Under
7 Q-Control
5 Times flight
29 Column Shift Right
HD-2 MC-DR Invert
17 E
Pick tfp Circuit
69-2-1,2 NC
14-1-1
CC-58
(14-15 1/3)
19-1-1 NC
18-1-1 NC
Cycle Ctr 9*s
Carry Contact
E Relay
17-l-(4)
Magnet
Hold Circuit
CC-36 (12-0)
ABP--27
17-1-4
Circuit Diagram
+69-2-1
£2=2-:
£j
14-1-1
"° r , CC-58 (14-15 1/3)
LS^l-l Cycle Ctr 9's
T Car ry Contact
"91 „
C C-36 (12-0)
10*
- MD-34
a:
JfflP=27
JW-U
^SLi
17-l-(4)
DIVISION CYC IE 11
This is a normal subtract cycle. If the E relay was picked up on the previous cycle, the F relay is now energized, whether or not the
previous cyclTwas a "no-go^ by means of the E relay and the F control relay. If the division has proceeded as far as the J^T Jg«
?CS relSr29-7,8,9-(12,12,o), shifting the DR to subtract from columns 4-27 of DD the G relay is picked up altering the read-out molding
of the cycle counter to molding C,, since thia counter has reached read-out position 19.
DIVISION CYCLE 11 -continued-
Magnet
56 Divide
71 Sign Control #2
14 MP-DIV Control Hold
HD-2 MC-DR Invert
5 Times Right
29 Column Shift Right
DD Counter Magnets
27 DD Carry Control
61 DD Carry
60 Elusive One
PQ Counter Magnets
64 F Control
65 G Control
17 E
18 F
19 G
8 Compare Control
Cycle Counter Magnet
3 Compare In
21 Column Shift Left
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-44 (2-1 1/3)
17-1-2
CC-44 (2-1 1/3)
29-9(2)-l
69-2-1,2 NC
14-1-1
CC-79 (6-5 2/3)
HD-2-11
17-1-1 or
CC-31 (12 3/2-9)
8-1-1
63-1-1
64-1-1
F Control
64-l-(4)
G Control
65-l-(4)
F Relay
18-l-(4)
CC-46 (2-13 1/3)
ABP-35
64-1-4
CC-46 (2-13 1/3)
ABP-35
65-1-4
12-1,2-2 NC or
CC-32 (8 1/2-2)
and
18-1-4
+ CC-44 (2-1 1/3)
c^J
_ lZ=l r 2
CC-46 (2-13 1/3)
H
sQ=
.64-1-4
ABP^35 t.
f .CC-44 (2-1 1/3)
H
^2=2i.2)-i
CC-46 (2-13 1/3)
<-MD-35
"F Control
64-l-(4)
- MD-35
"G'Control
65-l-(4)
+ 69-2- 1,2
CC-31 (J2 1/2-9)
12-1,2 -2
14-1- 1
CC-79 (6-5 1/3)
t_
,63-1-1
^h:
_jro-2-.11
CC-32 (^ 1/2-2)
HFT .
64-1-1
17-1-1
18-1-4
^J 18-l-(4)
DIVISION CYCLE 11 -continued-
Pick Up Circuit
69-2-1,2 NC
14-1-1
CC-60 (6-5 1/3)
HD-2-11
56-13-6
29-9-4
or
CC-31 (12 1/2-9)
8-1-1
63-1-1
65-1-1
G Relay
19-1-U)
Magnet
12-1,2-2 NC or
CC-32 (8 1/2-2)
and
19-1-4
Hold Circuit
Circuit Diagram
+^2=2-1
-14-1- 1
♦ .CC-60 (6-5 1/3)
DIVISION CYCLE 12
This cycle, a compare cycle, shows the pick lip of the "no-go" relay if the remainder standing in DD is less than all DR multiples for a
particular columnar position. Since the Q control relay is not picked up, the cycle counter is advanced and the cycle terminates by pick-
ing up the relays preliminary to another compare cycle*
Pick Up Circuit
CC— ^fl
(11-1/4 12)
3-24-10,12
Magnet
56 Dividti
71 Sign Control #2
14 I1P-DIV Control Hold
3 Compare In
21 Column Shift Left.
6 DD Corapars
2 DR Compare
63 No-Go
18 F
19 G
Cycle Counter Magnet
8 Compare Control
3 Compare In
29 Column Shift Right
Magnet
No-Go
63-l-(4)
Hold Circuit
CC-38 (11 1/2-9)
63-1-4
Circuit Diagram
+ CC-37 (11-1/4 12)
3^-10
t_
CC-36 (11 1/2-9) J3-24- 12 "
t _
j 63-l-(4)
DIVISION CYCLE 13
In this cycle division has been carried sufficiently far to arrive at the place limitation plugging and energize the "9" relay preliminary
to terminating the division. It is a compare cycle similar to all other compare cycles.
Magnet
9 9
56 Divide
71 Sign Control #2
14 MP-DIV Control Hold
18 F
19 G
3 Compare In
29 Column Shift Right
6 DD Compare
2 DR Compare
1 Over-Under
7 Q-Control
5 Times Right
29 Column Shift Right
HD-2 MC-DR Invert
Q It Oil
E
I
■
1
EE
1
1
1
[
[[
1
ECEX
1
■
Jg
I
■
1
|
■
■
■
IB
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
CC-44 (2-1 1/3)
56-13-5
29-3n-3 or
21-3n-3
Plug Wire
"9" Relay
9-1-U)
CC-48 (2-4)
9-1-4
+ CC-44 (2-1 1/3)
H , 56-13-5 29-3n-3 or
t , 21-3n-3 PIuk
CC-48 (2-4) t
. ^Wira. n _r MD-34
_H . o9-l-4
9-l-(4)
DIVISION CYCLE 14
The subtraction from DD and the entry of the digit of the quotient into the PQ counter are completed as in all subtract cycles. The "9"
relay permits the energizing of the A relay and the B relay also if the 47th column of PQ stands at 9. The energized A relay permits the
sequence mechanism to read setting up the sequence relays and in turn the storage counter in and repeat relays. Energizing of the A relay
will cause the MP-DIV control relay to drop out. This prevents further advance of the cycle counter and permits the sequence counter to
advance io read-out position 7. In preparation for the next cycle, under control of the sequence counter, the sequence counter reset, the
MC-DR reset, the Q-shift and the H relays are picked up. If the B relay is energized (a nine in the 47th column of PQ) the DD-PQ invert
relay is picked up. The MC-DR entry control (1-2), (3-6) and (4-8) relays are picked up under control of the MC-DR reset relay as in
multiplication cycle 9*
Pick Up Circuit
69-2-1,2 NC
14-1-1
CC-60 (6-5 1/3)
9-1-1
DIVISION CYCLE 2£ -continued-
CJI
Magnet
56 Divide
71 Sign conti'ol #2
14 MP-DIV Control Hold
18 F
19 G
HD-2 MC-DR Invert
5 Times Right
29 Column Shift Right
DD Counter Magnets
27 DD Carry Control
61 DD Carry
60 Elusive One
PQ Countei* Magnets
O II on
12 A
16 B
Seq-31 Control
Seq-B-6-1
Seq-B-4-1,2
Seq-C-7-1
Seq-27 Repeat
Sequence Counter Magnet
SC40-4,5,6 Storage Counter In
48 Sequence Counter Reset
47 MC-DR Reset
HD-5 MC-DR Reset
91 MC-DR Entity Control (1-2)
92 MC-DR Entiry Control (3-6)
93 MC-DR Entiy Control (4-8)
33 Q Shift
20 H
HD-3 DD-I»Q Iimrert
III
III
Magnet
A Relay
12-1, 2-(4)
CC-29 (6-8)
12-1-4
Hold Circuit
Circuit Diagram
6>2-2 1 t
-1-1
.CC-60 (6-5 V3)
CC-29 (6-8)
hL
-JMt*
T jU- n5 =,MD-34
A Relay
12-l-(4)
^MD-35
12-2-(4)
DIVISION CYCLE 14. -continued-
Pick Up Circuit
Magnet
Hold Circuit
Circuit Diagram
69-2-1,2 NC
14-1-1
CC-60 (6-5 1/3)
9-1-1
PQ 47th column
9' s Carry
Contact
14-1-4 NC
CC-55
(12 1/2-13 2/3)
Seq Ctr RO B-7
56-12-6
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-7
56-12-7
14-1-4 NC
CC-56
(12 1/2-13 2/3)
Seq Ctr RO C-7
56-12-7
CC-63 (12-0)
CC-33
(14-15 1/3)
48-1-8
56-13-9
Q-Shift Ctr RO
B Relay
l6-l-(4)
CC-29 (6-8)
16-1-4
Sequence Counter
Reset
48-l-(12)
MC-DR Reset
47-l,..,13-(12)
MC-DR Reset
HD-5-(12)
Q-Shift
33-1,.., 80-
(4,6 or 12)
CC-43 (12-0)
ABP-31-32-33
48-1-6
CC-43 (12-0)
ABP-31-32-33
47-13-10,11,12
CC-43 (12-0)
ABP-31-32-33
47-13-10,11,12
CC-63 (12-0)
CC-43 (12-0)
ABP-31
33-2n-12
+ j69-2- l
[69-2-:
£J
.14-1-1
t CC-60 (6-5 1/3)
H^
9-1-1 PQ 47th column
CC-29 (6-8)
n=T. 016-1-4
+ 9's C arry Contact
l6-l-(4)
WJ
+.J4-1-4
T* CC-55 (12 1/2-13 2/3)
o l o 2 o 3 o 4 o 5 o 6 Q 7 T8°9 o J6-12 -6
CC-43 (12-0) Seq Ctr RO B-7 °^ ♦"
1 LJ
48-1-6 - -
^-jjD-42
Sequence Counter Reset
48-l-(12)
+14-1-4
~~° f CC-56 (12 1/2-13 2/3)
H .
o l o 2 o 3 o 4 o 5°6 o 7 ^8 o 9 o J>6-12 -7
CC-43 (12-0) Seq Ctr RO C-7
H^
ABl€3l252^33
+JL4-1- 4
T CC-56 (12 1/2-13 2/3)
— n=f
^7-13-10,11,12
T^^sr* 2
Reset
47-l,..,13-(12)
o l o 2 o 3 o 4 o 5°6 o 7 ?8 o 9 o .56-12 -7
CC-43 (12-0) Seq Ctr RO C-7 * i~ CC-63 (12-0)
m
T8&rf%g5T
+ CC-33 (14-15 1/3)
^7-13- 10,11,12
m
"^- A ER£i>R"*Reset
HD-5-(12)
t ,
CC-43 (12-0)
\HL
o l o 2 o 3 o 4 o 5 o 6°7?8 o 9 c
ah%:
^3-211 -12 Q-Shift Ctr RO
t .
- UD-38
T^-ljS&jft
33-l,..,80-(4,6 or 12)
CJ1
to
en
DIVISION CYCLE 14. -continued-
Pick Up Circuit
CC-33
(14-15 1/3)
48-1-8
56-13-8
Magnet
H Relay
20-l-(4)
Hold Circuit
CC-43 (12-0)
20-1-4
Circuit Diagram
4 CC-33 (14-15 1/3)
^8-1-8
CC-43 (12-0)
'ABP%T"
56-13-8
20-1-4
a _- MD-34
20~l-(4)
D IVISION CYCLE 15
The quotient reads from the PQ counter to storage through th« Q-shift relay, except for column 47 which read through the H relay. The stor-
age counter carry is completed. The wequence counter, cycle counter, 47th column of the PQ counter and MC-DR counters reset. The repeat
relay permits the pick up of the start relay. The calculator continues in operation.
Magnet
HD-3 DD-PQ Invert
SC40-4,5,6 Storage Counter In
33 Q Shift
20 H
Storage Counter Magnets
SC40-9 Storage Counter Carry Control
SC40-7,8 Storage Counter Carry
12 A
16 B
48 Sequence Counter Reset
Sequence Counter Magnet
PQ 47th column Counter Magnet
Cycle Counter Magnet
47 MC-DR Reset
HD-5 MC-DR Reset
91 MC-DR Entry Control (1-2)
MC-DR Counter Magnets (1-2)
92 MC-DR Entry Control (3-6)
MC-DR Counter Magnets (3-6)
93 MC-DR Entry Control (4-8)
MC-DR Counter Magnets (4-8)
MC-DR Counter Magnets (5)
MC-DR Counter Magnets (7)
MC-DR Counter Magnets
Seq-27 Repeat
Seq-33 Start
Seq-31 Control
Seq Relays
(9)
II
III
■ I
■ I
1 1
1 1
1 1
1 1
DIVISION CYC^E IS -continued-
Pick Up Circuit
Magnet
CC-1,..,9
HD-3-l,..,9 NC
HD-3-10
HD-6-l,..,9 NC
PQ Counter RO
33-1-1,..,
33-80-11
Buss
SC40-4-1,..,
SC40-5-11
CC-9 (9-9 1/2)
HD-3-10
Col. 46 zero
Col. 47 zero or 8
HD-3-11
20-1-1
Buss
SC40-5-12
CC-2 (2-2 1/2)
71-1-3 NC
PQ 47th column
8 spot RO
20-1-2
CC-1 (1-1 1/2)
71-1-2 NC
PQ 47th column
spot RO
20-1-2
Storage Counter
Magnet (cols.
1-23)
Read 9 from 47th
col. of PQ to
24th col. of
storage counter
PQ 47th column
Counter Magnet
Hold Circuit
Circuit Diagram
+ CC-1, .., 9
-* -j=T ' HD-3-l ,..,9
Q — *- HD-6-l,..,9
HD-3- 10 |
Vl 2 3 4 ^6 7 8°9 Jw ll"
PQ Counter RO
^-Bdfc^E
SC40-4-1,..,
SC40-5-11
- F-14
Storage Counter Magnet
columns 1-23
+ CC-9 (9-9 1/2)
~ H=r HD-3-9
HD-6-1
^htf — i
col
.46 r~D^5 l o 6 o 2 o 7 o 3 o 8 o 4°
HD-?-ll
I
J__ ^ Storage Counter
T7T77TTI :i n 20 " 1 " 1 Magnet col.24
«"••*' y ^1 6 2 7°3 8 8 4 9 5 ? r . _ Q . -SC40-5-12
- F-14
+ CC-2 (2-2 1/2)
FT , 71-1 -3
CC-1 (1-1 1/2)
1
HU- ' '**"
~~1
o 5 o l o 6 o 2 o 7 o 3 o 8?4°9f
PQ 47th column
20-1-2
- MD-12
♦ - MU-JL2
^°Tqr47lh Column
Counter Magnets
Relay
l-l,..,423-(4) D
Over Under
D-6
2-l,..,2l6-(4) D
DR Compare
D-6
Row
1,..,9
1,..,9
3-l,..,18-(12) S
3-19,..,24-(12) S
3-25-C4) S
Compare In
D-5
4--l,..,27-(12,12,4) S
Tjjnes Left
M-5
5--l,..,27-(12,12,4) S
TJimes Right
M-5
D-6
1,..,9
19
21
1,..,9
1,..,9
Contact
1-1,.., 46-1
l-47-(4)
2 36 k — : 9
l-(47k-46),..,(47k)-l
1 £ i s; 423
l-i-3
2-2,. n., 23-1 NC
2-1, .n.. 23-2
2-24-U)
2s£ k s»9
2-(24k-22) , .n. , (24k)-l NC
2-(24k-23) , .n. , (24k)-2
IsSi 2S216
2-1-4
3-1-1,.., 3-2-11
2<;k =£9
3-(2k-l)-l,..,3-(2k)-IE
3-19-1,.., 3-20-12
3-19-1,.., 3-20-12 NC
3-19-1*.., 3-20-12 NC
3-21-1,.., 3-24-9
3-21-1,,.., 3-24-9 NC
3-21-1,.., 3-24-9 NC
3-24-10,12
3-24-llj 3-25-1,2
4-1-1,.., 4-2-11
4-(3k-2)-l, . . ,4-(3k-l)-12
4-3k-l
4-3k-4
5-1-1,.., 5-2-11
5-(3k-2)-l, . .,5-(3k-l)-12
5-3k-l
5-3k-2
5-3k-4
Cycle
D-6
D-6
D-6
D-6
D-6
D-6
D-6
D-6
D-6
D-6
D-6
11-6
D-7
D-6
M-6
D-6
D-6
D-12
D-5
M-6
M-6
M-6
M-5
M-6
D-6
M-6
D-6
M-6
D-7
D-7
M-5
D-6
Function
PU of Q-Control 7-1- (4)
Does not exist
PU of Q-Control 7-k-(4)
Hold
PU of Over Under l-2,.(2n-2).,44-(4)
PU of Over Under l-2,.(2n-l).,45-(4)
Does not exist
PU of Over Under l-(47k-45),.(2n-k-l).,(47k-l)-(4)
PU of Over Under l-(47k-46),.(2n-k).,(47k)-(4)
Hold
PU of DR Compare 2-l,..,23-(4)
PU of DR Compare 2-(24k-23),...24k-(4)
PU of DD Compare 6-1,. ,,24-(12)
Control read-in to FQ ctr magnets
Control read-in to DD ctr magnets
PU of DD Compare 6-l,..,24-(l2)
Control read-in to DD ctr magnets
Control read-in to DD ctr magnets
PU of Q-Control 7-l.,..,9-(4)
PU of No-GO 63-l-(4)
Hold
Control MC-DR times 1 RO to DD ctr magnets
Control MC-DR times k RO to DD ctr magnets
PU of DD Carry Control 27-l-(4)
Hold
Control MC-DR times 1 RO to PQ ctr magnets
Control MC-DR times 1 RO to DD ctr magnets
Control MC-DR times k RO to PQ ctr magnets
PU of PQ Carry Control 24-l-(4)
PU of DD Carry Control 27-l-(4)
PU of Elusive One 60-1, . . ,23-(4)
Controls Q Entry into PQ ctr
Hold
VI
CO
00
Relay
6-l,..,24-(12) D
DD Compare
D-6
7-l,..,9-(4) D
Q-Control
D-6
8-l-(4) S
Compare Control
D-5
9-l-(4) D
"9" Relay
D-13
10-1-U) S
LE
L-l-(6)
L-2-(4)
ll-l-(6)
11-
LP
12-l,2-(4) S
A
M-10
D-14
13-l-(6) S
MP-DIV Control Pick-Up
M-5
D-5
Row
10
10
10
10
10
10
10,11
10
Contact
6-1,.., 23-1
6-24-1
6-1, ,n.,24-k
6-1,.., 24-12
is k <9
7-(k)-l
7-(k)-2 NC
7-(k)-3
8-1-1
8-1-3,4
8-1-3,4 NC
9-1-1
9-1-4
10-1-1
10-1-2
10-1-3
10-1-4
11-1-1
11-1-2
11-1-3 NC
11-1-4
11-1-5
11-1-6
11-2-2- NC
12-1-1
12-1,2-2
12-1,2-3
12-1-4
13-1-1
13-1-2
Cycle
D-6
D-6
D-6
D-6
D-6
M-5
D-5
D-6
D-ll
D-5
D-6
D-14
D-13
M-5
D-5
M-7
D-ll
M-10
D-14
M-10
D-14
M-5
D-5
D-5
M-5
D-5
Function
PU of Over Under l-2,.(2n-2).,44-(4) or l-2,.(2n-l).,45-(4)
PU of Over Under l-46-(4)
PU of Over Under l-(47k-46),.(2n-k).,(47k)-(4)
or l-(47k-45) , . (2n-k-l) . , (47k-l)-(4)
Hold
PU of Times Right 5-(3k-2)-(12); 5-(3k-l)-(12); 5-(3k)-(4)
Controls read-in to Cycle ctr
Hold
PU of F 18-l-(4)j G 19-l-(4)
PU of Compare In 3-l,..,24-(12)j 3-25-(4)
PU of MC-DR Invert HD-2-(12)
PU of A 12-l,2-(4); B l6-l-(4)
Hold
Controls read-in to Log Cycle ctr
PU of MC-DR Reset 47-l,..,13-(12) (Log)
PU of LF ll-l-(6)j ll-2-(4)
Hold
PU of LIO In #1 189-1,2,3-(12,12,4)
Hold of LE 10-l-(4); LM 42-l,2,3-(12,12,4)
PU of Intermediate In 50-l,2,3-(l2) (Log)
Hold of LG 201-l-(4)
PU of Read Control Seq-31-(4) and Clutch Magnet (not used)
Hold
PU of Intermediate In 50-l,2,3-(12) (Log)
Controls read-in to Sine Sequence ctr #2
Hold of MP-DIV Control Hold 14-1-(12)
Hold of F 18-l-(4)
PU of Read Control Seq-31-(4) and Clutch Magnet
Hold
Controls read-in to Cycle ctr
PU of Compare Control 8-l-(4)
PU of MP-DIV Control Hold 14-1-(12)
to
CO
Relay
Row
13-l-(6) S
(continued)
14-1-(12) S
MP-DIV Control Hold
M-5
D-5
10
15-l-(4) 6
l6-l-(4) S
B
11-10
I>-14
17-l-(4) n
E
M-6
IW.0
18-l-(4) D
P
M-7
I>-11
10
10
10
10
10
Contact
13-1-3
13-1-4
13-1-5
13-1-6
14-1-1
14-1-2
14-1-3 NC
14-1-4 NC
14-1-5
14-1-9
14-1-11
15-1-1
15-1-2 NC
15-1-3,4
16-1-1
16-1-4
17-1-1
17'-l-2
17-1-4
iei-i-i
1&-1-2
l€t-l-4
Cycle
M-5
D-5
D-5
M-5
D-5
M-5
D-6
M-10
D-U
16-6
D-10
M-7
D-ll
M-8
D-7
D-6
M-0
E>-0
M-0
D-0
M-6
D-7
11-6
M-5
D-5
K-10
D-14
U-10
D-14
M-7
D-ll
D-ll
M-6
D-10
M-6
M-8
M-7
D-ll
Function
PU of MP-DIV Control Hold 14-1-(12)| Column Shift Right
29-l,..,36-(12,12,6)
PU of Compare In 3-l,..,24-(12); 3-25-C4)
PU of XJ 216-1-- (6); E Shift 213 and 214 (Exp)
Hold
PU of Column Shift Left. 21-1...,36-(12,12,6); Column Shift
Right 29-l,..,36-(12,12,6)
PU of A 12-l-(4)l B l6-l-(4)
PU of E 17-l-(4)
PU of F 18-l-(4)
PU of C 2 66-l-(4)j D 2 67-l-(4)
PU of Compare In 3-l,..,24-(12); 3-25-(4)
PU of MC-DR Invert HD-2-(12)
Controls read-in to Sequence ctr
Controls RO of Sequence ctr
Controls read-in to Cycle ctr
PU of Compare Control 8-l-(4); Controls read-in to Cycle ctr
Hold of PQ 23rd Col 68«l-(4)
Hold
Controls reset of Sequence ctr to 4 (Exp)
PU of MC-DR Reset 47-l»..,13-(12) (Exp)
Hold
PU of DD-PQ Invert HD-3-(12)
Hold
PU of F 18-l-(4)
PU of F Control 64-l-(4)
Hold
Controls Cyelei ctr RO A & B mldgs
Controls Cycle ctr RO D & D mldgs
Hold
en
O
Relay
Row
Contact
Cycle
Function
19-l-(4) D
10
19-1-1 NC
M-5
Controls Cycle ctr RO
G
D-5
D-ll
19-1-4
D-ll
Hold
20-l-(4) S
10
20-1-1
D-15
Controls RO of PQ 47th col
H
20-1-2
D-15
Controls reset of PQ 47th col
D-14
20-1-4
D-14
Hold
21-1,.. ,36-(12, 12,6) S
11
lss k sell
Column Shift Left
21-(3k-2)-l, . . ,21-(3k-l)-12
M-6
Control shift of multiple of MC-DR to cols 2k up of DD
M-5
D-7,8
D-7
21-34-1,.., 21-35-12
is n s=12
— —
Control shift of multiple of MC-DR to cols up of DD
21-3n-l
D-7
PU of Elusive One 60-1,.., 23-(4)
21-3n-2
D-7
Controls Q-Entry into PQ ctr
21-3n-3
D-13
PU of »9 n relay 9-l-(4)
21-3n-5
M-5
Controls MP ctr RO 2nd mldg
21-3n-6
M-5
Hold
22-l-(12) S
11
22-1-1,.., 10
D-2
Control Invert of Q-Shift ctr
Q-Shift Invert
22-1-11
D-l
Hold
D-l
23-l-(4) S
11
23-1-1
14-1
PU of Intermediate Carry 53-l,2-(12)
Intermediate Carry
23-1-4
H-l
Hold
Control
M-l
D-l
24-l-(4) S
11
24-1-1
M-6
PU of PQ Carry 62-lj..,4-(12)
PQ Carry Control
24-1-4
M-6
Hold
M-6
25-l-(4) S
11
25-1-1
D-4
PU of Q-Shift Carry 28-l-(4)
Q-Shift Carry Control
25-1-4
D-4
Hold
D-4
26-l-(4) D
11
26-1-1
M-3
PU of MC-DR Carry 49-l,..,10-(12)
MC-DR Carry Control
26-1-4
M-3
Hold
M-3
27-l-(4) S
11
27-1-1
M-6
PU of DD Carry 6l-l,..,4-(12)
DD Carry Control
27-1-4
M-6
Hold
D-4
en
CO
Relay
28-l-(4) S
Q-Shift Carry
D-4
29-l,..,36-(12,12,6) S
29-9(2)-(4)
Column Shift Right
M-5
D-5
30-l-(l2) D
C Relay
M-9
31-1-(12) D
D Relay
M-9
Row
11
12
12
12
12
32-1-U) S
Add-22
D-3
33-l,..,32-(12) S
33-33,.., 46-(12) S
33-47,.. ,70-(4,6 or 12) S
33-71,.., 80-(12) S
Q rShift
12
13
14
20
21
Contact
28-1-1,2
Uks 12
29-(3k-2)-l, . . ,29~(3k-l)-12
29-3k-l
29-3k-2
29-3k-3
29-9-4
29-3k-5
29-3k-6
29-9(2)-l
30-1-1,2 NC
30-1-3
30-1-4
30-1-5
30-1-6
30-1-7
30-1-8,9 NC
30-1-10 NC
30-1-1X
31-1-1,2 NC
31-1-3
31-1-4
31-1-5
31-1-6
31-1-7
31-1-8,9 NC
31-1-10 NC
31-1-11
32-1-1,2
32-1-3
32-1-4
2S k *■ 22
33-(45-2k)-l, . . ,33-(46 -2k)-12
Osi k ssil
33-(47 + k)-(4,6 or 12)
Cycle
D-1,4
M-6
D-5
D-7
D-7
D-13
D-ll
M-5
M-5
D-5
D-ll
M-5
M-9
M-5
M-8
M-9
M-5
M-9
M-5
M-8
M-9
D-4
D-4
D-3
D-15
D-15
Function
C7I
CO
to
Control Q-Shift Carry
Control Multiple by (2k-l)st col of MP to cols (2k-l) up of
PQ or DD
PU of Elusive One 60-l,..,23-(4)
Controls Q-Entry into PQ ctr
PU of "9" relay 9-1- (4)
PU of G 19-1~(4)
Controls MP ctr RO 2nd mldg
Hold
PU of G Control 65-l-(4)
Hold of MP Cycle Control Hold 37-l,..,26-(4,6 or 12)
PU of DD-PQ Transfer #2 59-l,2-(12)j 59-3-(6); MP Reset
40-l,2,3-(12)j MC-DR Reset 47-1, ..,13-(12); MC-DR Reset
HD-5-(12)
Controls RO of Log Cycle ctr
PU of EIO Reset 218-1,2,3-(12)
Controls RO of Sine Sequence ctr #1
PU of Intermediate In 50-l,2,3-(12) (Log)
Hold of MP Cycle Control Hold 37-l,..,26~(4,6 or 12)
PU of C 2 66-1- (4)
Hold
Hold of MP Cycle Control Hold 37-l,..,26-(4,6 or 12)
PU of DD-PQ Transfer #2 59-l,2-(12); 59-3-(6)j MP Reset
40-l,2,3-(12); MC-DR Reset 47-1,. ,,13-(12) j MC-DR Reset
HD-5-(12)
Controls RO of Log Cycle ctr
PU of EIO Reset 218-1,2,3-(12)
Controls RO of Sine Sequence ctr #1
PU of Intermediate In 50-l,2,3-(12) (Log)
Hold of MP Cycle Control Hold 37-l,..,26-(4,6 or 12)
PU of D2 67»l-(4)
Hold
Control read-in to Q-Shift ctr
PU of Q-Shift Carry Control 25-l-(4)
Hold
Control shift of PQ RO k cols to right
Control supply of k nines to left of PQ-RO
Relay
Row
Contact
Cycle
Function
(continued)
33-l,..,32-(12) S
12 ^ k s: 22
33-33,.., 46-(l2) S
33-(35 + 2k)-l,..,
D-15
Control supply of k nines to left of PQ RO
33-47,.., 70-(4,6 or 12) S
33-(36 + 2k)-3,5 or 11
33-71,.., 80-(12) S
OSksll
Q-Shift
33-(47 + k)-4,6 or 12
D-15
Hold is last point
D-14
12 =£ k =s 22
33-(36 + 2k)-4,6 or 12
D-15
Hold is last point
34-l,2,3-(12) S
14
34-1-1,.., 34-2-12
M-ll
Control PQ ctr RO
34-4-(4)
14
34-3-1
PU of LIO In #1 192-1,2,3-(12,12,4)
P-Out
34-3-2
- -
PU of Divide 56-1, . .,13-(12) (Exp)
M-10
34-3-3 NC
- -
Hold of Tape Selection Relays 183,184,185-1,. .,9-(l2)
(Int)
34-3-5 NC
- -
Hold of LG 201-l-(4)
34-3-6
PU of SM-3 83-l,2-(12,4)
34-3-7 NC
- -
Hold of SM-3 83-l,2-(l2,4)
34-3-8
- -
PU of Read Control Seq-31-(4) and Clutch Magnet (not
used)
34-3-9
M-ll
Controls reset of PQ 47 col
34-3-12} 34-4-4
M-10
Hold
35-l,..,46-(4) S
14
35-45,46-1 NC
M-l
PU of Shift 36-37 ,38,39-(12,12,4) (No shift)
Shift Pick-Up
35-45-1; 35-43,44-1 NC
D-l
PU of Shift 36-34,35, 36-(12,12,4) (Shift 1 col)
D-l
35-45,43-1; 35-41,42-1 NC
D-l
PU of Shift 36-32,33-(12) (Shift 2 cols)
M-l
3 * k < 13
35-45,. (2n +l).,(47-2k)-l;
D-l
PU of Shift 36-(36-2k),(37-2k)-(12,4,6 or 12) (Shift
k cols)
35-(45-2k),(46-2k)-l NC
14 £ k £ 22
35-45,. (2n + l).,(47-2k)-lj
D-l
PU of Shift 36-(23-k)-(4,6 or 12) (Shift k cols)
35-(45-2k),(46-2k)-l Nc
35-n-4
D-l
Hold
36-l,..,39-(4,6 or 12) S
15
Controls shift of k cols to left; last two points read amount
Shift
of shift to Q-Shift ctr
M-l
k - 20,21,22
D-l
36-(23-k)-l,..,(25-k)
15 £ k ss 19
M-2
D-2
Hold is last point
36-(23-k)-l,..,(25-k)
M-2
Hold is 36-(23-k)-ll
k =14
D-2
36-(23-k)-l,..,(25-k)
M-2
Hold is 36-(23-k)-12
8^ kil3
D-2
36-(36-2k)-l,..,
M-2
Hold is last point
36-(37-2k)-(13-k)
D-2
3^ k^7
36-(36-2k)-l,..,
M-2
Hold is 36-(37-2k)-ll
36-(37-2k)-(13-k)
k= 2
36-32-1,.., 36-33-11
D-2
M-2
Hold is 36-33-12
D-2
Relay
36-l,..,39-(4,6 or 12) S
(continued;
37-l,..,26-(4,6 or 12) D
Iff' Cycle Control
M-5
3&-l,2,3-(12) S
Multiply #2
M-0
3S»-1,2,3-(12) S
MP In
M-4
Row
16
16
16
Contact
k -1
36-34-1,.., 36-3 5-12
k-
36-37-1,.., 36-39-1
1 £ k £12
37-1-1
37-3-1
3< k £12
37-(k + 2)-l
37-14-2 NC
2 £ k £ 11
37-16-1
37-(k + 15)-1
37-26-2 NC
37-2,4-3; 37-5,.., 10-12?
37-11,12-6; 37-13,14-4;
37-16-3; 37-17,.., 22-12;
37-23,24-6; 37-25,26-4
38-1-1, ..,38-2-1
38-2-2, „., 38-3-1
38-3-3
38-3-5
38-3-6
38-3-7
38-3-8
38-3-11
39-1-1, ,,.,39-2-11
39-2-12
39-3-1 NC
39-3-2
39-3-3
39-3-4
39-3-5
39-3-6
39-3-7
39-3-8 IK
39-3-9
Cycle
H-2
D-2
M-2
D-2
M-5
M-5
M-5
M-8
M-5
M-5
M-8
M-5
M-5
M-8
M-5
M-8
M-0
M-7
M-5
M-6
M-6
M-0
M-5
M-5
Function
Hold is 36-36-4
Hold is 36-39-2
A digit in col 1 of MP picks up 37-l,2-(12,4)
A digit in col 3 of MP picks up 37-3,4-(12,4)
A digit in col (2k-l) of MP picks up 37-(k + 2)-(4,6 or 12)
in order to read to PQ col (2k-l) and up
PU of 29-l,2 J( 3-(12,12,6) Column Shift Right
PU of 29-4,5„6-(12,12,6) Column Shift Right
PU of 29-(3k-.2),(3k-l),(3k)-(12,12,6) Column Shift Right
PU of D 2 67-l-(4)
A digit in col 2 of MP picks up 37-15,l6-(12,4)
A digit in col 2k of MP picks up 37-(k + 15)-(4,6 or 12)
in order to read to DD col 2k and up
PU of 21-1,2;,3-(12,12,6) Column Shift Left
PU of 21-(3k-2),(3k-l),(3k)-(12,12,6) Column Shift Left
PU of C 2 66-l-(4)
Hold
PU of Column Shift Right 29-l,..,36-(12,12,6)
PU of D 2 67-l-(4)
PU of Column Shift Left 21-1,..,33-(12,12,6)
PU of C 2 66-l-(4)
Controls read-in to Sequence ctr
PU of F 18-l»-(4)
Control Cyclo ctr RO
PU of PQ Carry Control 24-l-(4)
PU of DD Carry Control 27-l-(4)
Hold
Control read-in to MP ctr and PU of MP Cycle Control
37-l,..,26-(4,6 or 12)
PU of MD-DIV Control Pick-Up 13-l-(6) "
Hold of Xm Step Control 180-l-(6) (Int)
PU of Sign Control #1 70-l-(4) (Int)
PU of SIO Reset 228-l,2,3-(12)
Controls read-in to. Log Cycle ctr
PU of LF ll-l,2-(6,4)
Controls reset of Xij, ctr (Int)
Controls read-in to Sine Sequence ctr #1
Hold of SIO Out #2 Control 237-l-(4)
PU of Forward Tape Clutch Magnet
Relay
Row
Contact
Cycle
Function
39-1,2,3(12) S
39-3-10
_ _
Controls read-in to X™ ctr (Int)
(continued)
39-3-11
M-4
Hold
39-3-12
PU of EIO 24th Col 9 225-1-6
40-l,2,3-(12) S
16
40-1-1,.., 9
M-10
Controls read-in of 10' s complements for MP reset
MP Reset
40-2-1,.., 40-3-11
M-10
Controls read-in to MP ctr
M-9
40-2-1,.., 40-3-11 NC
M-5
Controls read-in to MP ctr
40-3-12
M-9
Hold
41-1,2-(12) S
16
Controls Sequence ctr RO
Multiply #1
41-1-1
M-0
PU of Intermediate In 50-l,2,3-(12)
M-0
41-1-2
M-0
PU of DD-PQ Reset 58-l,..,8-(12)
41-1-3
M-l
PU of MC-DR In 43-1,. .,10-(12); 43-ll,12-(4)
41-1-4
M-l
PU of Intermediate Invert Control 94-l-(4)
41-1-5
M-2
PU of First Build Up 44-1,. .,5-(12)
41-1-6
M-2
PU of First and Second Build Up 45-1,.., 5- (12)
41-1-7
M-2
PU of Intermediate Reset 52-l,2,3-(12); HD-4-(12)
PU of Intermediate In 50-l,2,3-(32)
41-1-8
M-3
41-1-9
M-3
PU of First and Second Build Up 45-l...,5-(12)
41-1-10
M-3
PU of Second Build up 46-1, . .,5- (12)
41-1-11
M-4
PU of MP In 39-l,2,3-(12)
41-1-12
M-4
PU of Intermediate Invert Control 94-l-(4)
41-2-1
M-5
PU of Intermediate Reset 52-l,2,3-(12); HD-4-(12)
PU of Sequence Counter Reset 48-l-(12)
41-2-2
M-10
41-2-3
M-10
PU of P-Out 34-l,2,3-(12)j 34-4-(4)
41-2-4
M-9
PU of MC-DR Reset 47-1,. .,13-(12); HD-5-(12)
41-2-5
M-0
PU of Multiply #2 38-l,2,3-(12)
PU of P-Out 34-l,2-(12); 34-4-(4)
41-2-6
M-10
41-2-11
M-9
Hold
42-l,2,3-(12,12,4)
17
42-1-1,.., 42-2-3
_ «.
Controls Sequence ctr RO (Log)
LM
42-2-4
_ _
Hold of LE 10-l-(4)
42-2-5 NC
- _
Controls Sequence ctr reset (Log)
42-2-6
PU of Intermediate In 50-l,2,3-(12) (Log)
42-2-7 NC
- -
Controls RO of LIO 23rd col
42-2-8
- -
PU of Multiply #2 38-l,2,3-(12) (Log)
42-2-9 NC
- -
PU of Log In #2 190-1,2,3-(12,12,4)
42-2-10
- -
PU of Log Sine P-Out 72-1, 2,3- (12, 12, 4)
42-2-11
- -
Hold
42-2-12
- -
PU of Log Reset 191-1,2, 3-(12)
42-3-2
- -
Controls read-in to Log Cycle ctr
43-l,..,10-(12) S
17
43-1-1,.., 43-2-11
M-2
Controls entry into MC-DR (1-2)
43-ll-(4) S
16
D-2
43-12-(4) S
15
43-2-12
M-l
PU of Shift 36-37,38,39-(12,12,4)
MC-DR In
D-l
PU of Shift 36-l,..,39-(4,6 or 12)
M-l
43-3-1,.., 43-4-11
M-2
Controls entry into MC-DR (3-6)
D-l
Relay
Row
Contact
Cycle
Function
(continued)
43*1,.., 10-(12) S
43-4-12
D-2
PU of Q-Shift Elusive One Control 87-l-(4)
43-Il-(4) S
43-5-1,.., 43-6-11
M-2
Controls entry into MC-DR (5)
43-12-U) S
43-6-12
M-2
PU of Sign Control #1 70-l-(4)
MC-DR In
43-7-1,.., 43-8-11
M-2
Controls entry into MC-DR (7)
M-l
43-9-1,.., 43-10-11
M-2
Controls entry into MC-DR (9)
D-l
43-10-12
M-l
D-l
Hold
43-11-1
PU of SIO Out #2 Control 237-l-(4)
43-11-2
- -
Controls read-in to X T ctr (Int)
43-11-3
_ -
PU of Forward Tape Clutch Magnet (Int)
43-11-4
M-2
PU of Sign Control #2 71-l-(4)
43-12-1
M-l
PU of MC-DR Entry Control (1-2) 91-1,2,3-(12)
43-12-2
M-l
PU of MC-DR Entry Control (3-6) 92-l,2,3-(12)
43-12-3,4
M-l
D-l
Hold
44-l,..,5-(12) S
17
44-1-1,.., 44-2-12
M-3
Control MC-DR times 2 RO to MC-DR (3-6)
First Build Up
D-3
M-2
44-3-1,.., 44-4-12
M-3
Control MC-DR times 2 RO to MC-DR (9)
13-2
D-3
44-5-1
M-3
D-3
PU of Read Control Seq-31-(4) and Clutch Magnet
44-5-2
Controls read-in to Log Cycle ctr
44-5-5
- -
PU of SIO In #2 230-l,2,3-(12,12,4)
44-5-6
—
PU of 1T278-1,2,3-(12,12,4) (Sine)
44-5-7
- -
Controls read-in to Sine Sequence ctr #1
44-5-8
M-2
D-2
PU of MC-DR Entry Control (3-6) 92-l,2,3-(12)
'44-5-9
PU of Log Reset 191-1,2,3-(12)
44-5-11
M-2
D-2
Hold
45-l,..,5-(12) S
17
45-1-1,.., 45-2-12
M-3, 4
Control MC-DR times 2 RO to MC-DR (4-8)
First and Second Build Up
D-3,4
M-2
45-3-1,.., 45-4-12
M-3, 4
Control MC-DR times 2 RO to MC-DR (5)
D-2
D-3,4
45-5-1
M-3, 4
D-3,4
M-2,3
Controls MC-DR Carry Control 26-l-(4)
45-5-2
Controls MC-DR Entry Control (4-8) 93-l,2,3-(12)
D-2,3
45-5-3
- -
Controls read-in to Sine Sequence ctr #2
45-5-H
M-2
D-2
Hold
46-1,.., 5- (12) S
17
46-1-1,.., 46-2-12
M-4
Control MC-DR times 6 RO to MC-DR (7)
Second Build Up
46-3-1,.., 46-4-12
M-4
Control MC-DR times 6 RO to MC-DR (9)
M-3
46-5-1
Controls RO of Log Cycle ctr
Relay
Row
Contact
Cycle
Function
46-l,..,5-(12) S
46-5-2
NR-4
Controls read-in of 1 from Normalizing Register to
(continued)
Intermediate ctr
46-5-3
- -
Controls RO of Sine Sequence ctr #1
46-5-4
PU of SIO Out #3 272-l,2,3-(l2,12,4)
46-5-5
- —
Controls entry of 1 into Intermediate ctr 21st col (Exp)
46-5-11
M-3
Hold
47-l,..,13-(12) S
17,18
47-1-1,.., 47-2-11
M-10
Control reset of MC-DR (1-2)
MC-DR Reset
47-2-12
M-10
Controls reset of Cycle ctr
M-9
47-3-1,.., 47-4-12
M-10
Control reset of MC-DR (3-6)
D-14
47-5-1,.., 47-6-12
M-10
Control reset of MC-DR (4-8)
47-7-1,.., 47-8-12
M-10
Control reset of MC-DR (5)
47-9-1,.., 47-10-12
M-10
Control reset of MC-DR (7)
47-11-1,.., 47-12-12
M-10
Control reset of MC-DR (9)
47-13-1 NC
M-2
Hold of Sign Control #2 71-l-(4)
47-13-2
M-9
PU of MC-DR Entry Control (1-2) 91-1,2,3-(12)
47-13-3
M-9
PU of MC-DR Entry Control (3-6) 92-l,2,3-(12)
47-13-4
M-9
PU of MC-DR Entry Control (4-8) 93-l,2,3-(12)
47-13-10,11,12
M-9
Hold
48-l-(12) S
17
48-1-1 NC
M-0
Hold of Multiply #1 41-1,2-(12); Multiply #2 38-l,2,3-(12)
Sequence Counter Reset
D-0
Hold of Divide 56-l,..,13-(12)
M-10
- -
Hold of LM 42-l,2,3-(l2,12,4); IE 10-l-(4)j LF ll-l,2-(6,4) J
D-14
EX-2 55-1,2,3-(12,12,6)j SM-1 81-l,2,3-(12,12,4)j
IM-1 78-l,2,3-(l2,12,4)} IM-2 79-l,2-(12,4) J SM-5 85-l-(4)
48-1-2
M-ll
Controls Sequence ctr reset
48-1-3
PU of Log In #2 190-1,2,3-(12,12,4)
48-1-4
- _
PU of EX-2 55-l,2,3-(12,12,6)
48-1-5
- -
Controls reset of Sine Sequence ctr #1
48-1-6
M-10
Hold
48-1-7
PU of Read Control Seq-31-(4) and Clutch Magnet (Int)
48-1-8
D-14
PU of Q-Shift 33-l,..,80-(4,6 or 12); H 20-l-(4)
49-1,.., 10- (12) S
18
49-1-2,.., 49-2-12
M-3
Control Carry in MC-DR (3-6)
MC-DR Carry
49-3-2,.., 49-4-12
M-3
Control Carry in MC-DR (4-8)
M-3
49-5-2,.., 49-6-12
M-3
Control Carry in MC-DR (5)
D-3
49-7-2,.., 49-8-12
M-3
Control Carry in MC-DR (7)
Control Carry in MC-DR (9;
49-9-2,.., 49-10-12
M-3
50-l,2,3-(l2) s
18
50-1-1,.., 50-2-12
M-l
Control entry into Intermediate ctr
Intermediate In
50-3-1
M-l
PU of Intermediate Carry Control 23-l-(4)
M-0
50-3-11
M-0
Hold
D-0
51-1,2,3-(12) S
18
51-1-1,.., 51-2-12
_ «.
Control RO of Intermediate ctr (Int) (not used in MP-DIV)
Intermediate Out
51-3-1
PU of EIO In 217-1,2,3-(12,12,4)
PU of IM-3 80-l-(4) (Int)
51-3-2
- -
Ol
51-3-11
Hold
CO
Relay
52-l : ,2,3-(02) S
Intermediate Reset
M-2
D--2
53-l,2-(12) S
Intermediate Carry
K-l
54-l-(X2) S
EX-1
55-l,2,3-(12,12,6) S
EX-2
Row
18
18
18
56-l,..,13-(12) S
Divide
D-0
18
19
Contact
52-1-1,.., 52-2-11
52-2-12
52-3-1
52-3-2
52-3-3
52-3-4 NC
52-3-5
52-3-6 NC
52-3-7
52-3-H
53-1-1,.., 53-2-12
54-1-1,.., 5
54-1-6
54-1-7
54-1-8
54-1-9 NC
54-1-11
55-1-1,.., 55-2-3
55-2-4
55-2-5
55-2-6
55-2-6 NC
55-2-7
55-2-8
55-2-9 NC
55-2-10
55-2-11
55-2-12
55-3-1
55-3-2 NC
55-3-3
55-3-6
56-1-1,.., 56-2-12 NC
56-3-1,.., 56-6-10
56-7-1,.., 56-8-11
56-9-1,. (2n+ 1).,U,..,
56-10-11
56-9-2,. (2n)., 12,..,,
56-10-10
Cycle
M-3
M-2
M-3
M-2
M-6
D-6
I)-7
M-6
I)-7
D-6
D-8
Function
Control reset of Intermediate ctr cols 1-23
PU of C-6 Step Control 223-l-(4) (Exp)
PU of C Value to Intermediate Control 90-l-(4) (Int)
PU of MC-DR Reset Control #2 238-l-(12) (Sine)
PU of Value Tape Read Clutch Magnet
Hold of BI-1 7«-l,2,3-(12,12,4); IM-2 79-l,2-(12,4)
Controls reset of Intermediate ctr 24th col
Hold of Sign Control #1 70-l-(4)
Controls read-in to PQ 47th col
Hold
Control carry into Intermediate ctr cols 1-24
Control Sequence ctr RO (Exp)
PU of Multiply #2 38-l,2,3-(l2) (Exp)
PU of EIO 1-18 Out 219-l,2-(12)j EIO In 217-1,2,3-(12 J ,12,4)
PU of EX-2 55-l,2,3-(l2,12,6)
PU of C-6 Step Control 223-l-(4) (Exp)
Hold
Control Sequence ctr RO (Exp)
PU of Multiply #2 38-l,2,3-(12) (Exp)
PU of EIO 1-18 Out 219-1,2-(12)
Hold of EX-1 55-l-(12)
Hold of XG 15-l-(4)
PU of C-6 Step Control 223-l-(4) (Exp)
PU of Intermediate In 50-l,2,3~(12) (Exp)
Controls reset of Sequence ctr (Exp)
PU of XG 15-l-(4)
Hold of RO Control 226«l-(4); XH 220-l-(l2)
Hold
PU of MC-DR Ret3et 47-1, . .,13-(12) (Exp)
PU of Read Control Seq-31-(4) and Clutch Magnet
PU of Exp P-Out 73-1, 2- (12)
Hold
Control Linking of Times Left and Column Shift Left to DD ctr
Control PU of DD compare 6-l,..,24-(12)
Control read-in to DD ctr
Control read-in to PQ ctr
Control Q entry into PQ ctr
PU of Column Shift Right 29-1,. .,36-(12,12,6)
PU of Column Shift Left 21-1, . .,36-(12,12,6)
Relay
Row
Contact
Cycle
Function
56-l,..,13-(12) s
56-11-1
D-0
PU of Intermediate In 50-l,2,3-(12)
(continued)
56-11-2
D-0
PU of DD-PQ Reset 58-1, . ,,8-(12)
56-11-3
D-l
Controls RO of Intermediate ctr 24th col 2nd mldg
56-11-4
D-l
PU of MC-DR In 43-l,..,10-(12)j 43-ll,12-(4)
56-11-5
D-l
PU of Q-Shift Invert 22-l-(12)
56-11-6
D-l
PU of Intermediate Invert Control 94-l-(4)
56-11-7
D-2
PU of First Build Up 44-l,..,5'-(12)
56-11-8
D-2
PU of First and Second Build Up 45-l,..,5-(l2)
56-11-9
D-2
PU of Intermediate Reset 52-l,2,3-(12)j HD-4-(12)
56-11-10
D-3
PU of Intermediate In 50-l,2,3-(12)
56-11-11
D-3
PU of First and Second Build Up 46-1, ,.,5-(12)
56-12-1
D-3
PU of Add-22 32-l-(4)
56-12-2
D-4
Controls RO of Intermediate ctr 24th col 2nd mldg
56-12-3
D-4
PU of DD In 57-l,2,3-(12)
56-12-4
D-4
PU of Intermediate Invert Control 94-l-(4)
56-12-5
D-5
PU of Intermediate Reset 52-1,2, 3-(12)
56-12-6
D-14
PU of Sequence ctr Reset 48-l-(l2)
56-12-7
D-14
PU of MC-DR Reset 47-1, . .,13-(12); HD-5-(12)
56-13-1
D-0
Controls read-in to Sequence ctr
56-13-2
D-5
D-6
PU of Compare In 3-1, ..,24-(l2); 3-25-(4)
PU of MC-DR Invert HD-2-(l2)
56-13-3
D-7
PU of Elusive One 60-1, . ,,23-(4)
56-13-4
D-7
PU of DD Carry Control 27-l-(4)
56-13-5
D-13
PU of "9" 9-l-(4)
56-13-6
D-ll
PU of G 19-l-(4)
56-13-7
- -
Controls RO of Cycle ctr after PU of G relay
56-13-8
Controls carry from doubling RO of MC-DR (1-2) 23rd col
56-13-9
D-14
PU of Q-Shift 33-l,..,80-(4,6 or 12); H 20-l-(4)
56-13-11
D-0
Hold
57-l,2,3-(12) S
19
57-1-1,.., 57-2-11
D-5
Control entry into DD ctr
DD In
57-2-12
D-4
PU of Shift 36-l,..,39-(4,6 or 12)
D-4
57-3-1
D-5
PU of Q-Shift Carry Control 25-l-(4)
57-3-2
K-2
PU of Sign Control #1 70-1- (4)
57-3-4
D-5
PU of MP-DIV Control Pick-Up 13-l-(6)
57-3-11
D-4
Hold
58-l,..,8-(12) S
19
58-1-1,.., 58-4-10
M-l
Control PQ ctr reset
DD-PQ Reset
58-4-11,12
M-0
Hold
M-0
58-5-1,.., 58-8-9
M-l
Control DD ctr reset
D-0
58-8-10,11
D-l
Control Q-Shift reset
58-8-12
M-0
Hold
59-l,2,3-(l2,12,6) S
19
59-1-1,.., 59-2-11
M-10
Control DD cols 23-45 transfer to PQ
DD-PQ Transfer #2
59-3-1
M-10
PU of PQ Carry Control 24-l-(4)
M-9
59-3-2
M-10
PU of A 12-l,2-(4)j B l6-l-(4)
Ol
CO
Relay
59-l,2,3-(12,12,6) S
(continued)
60-l,..,,23-(4) S
Elusive One
D-7
6l-l,..,,4-(12) S
DD Carry
M-6
D-7
62-l,..,4-(12) S
PQ Carry
M-6
63-1-U) D
No Gk>
D-12
64-l-(4) S
F Control
D-ll
65-l-(4) S
G Control
D-ll
66-l-(4) D
C 2
M-8
67-1- (4) D
M-8
68-l-(4) D
PQ 23rd Column
M-6
69-l,2-(4) S
CD Control
M-9
Row
20
20
20
10
12
12
13
13
13
14
Contact
59-3-3
59-3-6
60-n-l
60-n-2
60-n-4
61-1-1,.., 61-4-9
62-1-1,,., 62-4-9
63-1-1
63-1-4
64-1-1
64-1-4
65-1-1
65-1-4
66-1-1
66-1-4
67-1-1
67-1-4
68-1-1
68-1-4
69-1-1
69-1-2
69-1-3
69-1-4
69-2-1,2 NC
Cycle
M-10
M-9
D-7
D-7
D-7
M-6
M-6
D-ll
D-12
D-ll
D-ll
D-ll
D-ll
M-8
M-8
M-8
M-8
M-6
M-6
M-9
M-6
M-8
M-9
M-5
M-6
M-7
M-8
Function
Controls res€>t of Cycle ctr
Hold
Controls entry of 1 into col n of DD ctr
Controls prevention of carry to the right in DD ctr
Hold
Control DD carry
Control PQ carry
PU of F 18-l-(4); G 19-l-(4)
Hold
PU of F 18-l-(4)
Hold
PU of G 19-l-(4)
Hold
PU of DD-PQ Transfer #1 74-l,2,3-(12,12,4)
Hold
PU of DD-PQ Transfer #1 74-l,2,3-(12,12,4)
Hold
Controls carry to PQ 23rd col
Hold
PU of C 30-l-(12)j D 31-1-(1?0
PU of PQ 23rd Column 68-l-(4)
Hold of C 2 66-l-(4); D 2 67-l-(4)
Hold
PU of MP-DIV Control Hold 14-1-(12) ; Column Shift Left
21-1,.., 27-( 12,12,6); Column Shift Right 29-l,.. 1 ,27-(l2,12,6)
PU of E 17-l-(4)
PU of F 18-!~(4)
PU of C 2 66- l-(4); D 2 67-l-(4)
Relay
Row
Contact
Cycle
Function
70-1-U) D
19
70-1-1
M-3
Controls read-in to PQ 47th col
Sign Control #1
70-1-2
M-2
PU of Sign Control #2 71-l-(4)
M-2
70-1-4
M-2
Hold
71-1- (4) D
20
71-1-1; 71-1-2,3 NC
M-ll
Control reset of PQ 47th col
Sign Control #2
M-2
71-1-4
M-2
Hold
72-l,2,3-(12,12,4) S
21
72-1-1,.., 72-2-12
_ _
Control RO of PQ ctr (Log-Sine)
Log Sine P-Out
72-3-4
- -
Hold
73-l,2-(12) S
21
73-1-1,.., 73-2-9
— —
Control RO of PQ ctr (Exp)
Exp P-Out
73-2-12
Hold
74-l,2,3-(12,12,4) D
21
74-1-1,.., 74-2-10
M-9
Control DD cols 1-22 transfer to PQ
DD-PQ Transfer #1
74-2-11
M-9
PU of CD Control 69-l,2-(4)
M-8
74-3-1
M-9
PU of PQ Carry Control 24-l-(4)
74-3-4
M-8
Hold
75-l,2,3-(l2,12,4) S
21
75-1-1,.., 75-2-12
_ _
Control read-in of C Value to Intermediate ctr
C Value to Intermediate
#1
75-3-4
— -
Hold
76-l,2,3-(12,12,4) S
21
76-1-1,.., 76-2-12
— _
Control read-in of C Value to Intermediate ctr
C Value to Intermediate
#2
76-3-4
— —
Hold
77-l,2,3-(12,12,4) S
21
77-1-1,.., 77-2-12
— „.
Control r ead-in of C Value to Intermediate ctr
C Value to Intermediate
#3
77-3-4
— —
Hold
78-l,2,3-(12,12,4) S
21
78-1-1,.., 76-2-4
...
Control RO of Sequence ctr (Int)
IM-1
78-2-5
- -
Controls Forward Tape Clutch Magnet
78-2-6
- -
Controls read-in to Xm ctr (Int)
PU of Multiply #2 38-l,2,3-(12) (Int)
78-2-7
78-2-8 NC
- -
Controls Read Control Seq-31-(4) and Clutch Magnet
78-2-9
- -
Hold of 3L, Step Control 180-l-(6)
Controls reset of Sequence ctr to 4 (Int)
78-2-10
78-2-11
Holdj hold of IM-2 79-l,2-(12,4)
78-2-12
_ -
PU of C Value to Intermediate Control 90-l-(4)
78-3-1
- -
PU of IM-2 79-l,2-(12,4)
78-3-2
PU of P-Out 34-l,2,4-(12,12,4) (Int)
78-3-4
- -
Hold
79-1, 2-( 12,4) D
21
79-1-1,2,3
_ _
Control Sequence ctr R0 (Int)
Bt-2
79-1-4 NC
Controls read-in to X~ ctr
Controls X T reset
PU of MC-DR Reset 47-1,.., 13- (12) (int) '
79-1-5
79-1-6
Relay
Row
Contact
79-l,2-(12,4) D
79-1-7
(continued)
79-1-8
79-1-9 NC
79-1-10 NC
79-1-11 NC
79-1-12
79-2-1 NC
79-2-4
80-l-(4) S
21
80-1-1
BI-3
80-1-4
81»1,2,3-(12,12,4) S
21
81-1-1,.., 81-2-3
SM-1
81-2-4
81-2-5
81-2-6
81-2-8
81-2-9 NC
81-2-10
81-2-H NC
81-2-12
81-3-1 NC
81-3-2 NC
82-l-(12) D
21
82-1-1 NC
SM-2
82-1-2
82-1-3
82-1-4
82-1-5
62-1-6 NC
82-1-7 NC
82-1-8
82-1-9 NC
82-1-11 NC
82-1-12
83-l,2-(l2,4) S
21
83-1-1 NC
SM-3
83-1-2
83-1-3
83-1-4
83-1-5
83-1-6 NC
83-1-7
83-1-8
83-1-9
Cycle
Function
PU of Read Control Seq-31-(4) and Clutch Magnet
Controls Forward Tape Clutch Magnet
Hold of Xp Step Control 180-l-(4)
Controls reset of Sequence ctr to (Int)
Hold; hold of B£-l 78-l,2,3-(l2,12,4)
PU of IM-3 80-l-(4)
Hold of Tape Selection Relays 183, 184, 185-1,.., 9--(12)
Hold
Controls Sequence ctr reset (Int)
Hold
Control Sequence ctr RO (Sine)
Hold of SM-1; Multiply #2 38-l,2,3-(12) (Sine)
PU of MC-DR Reset 47-1,. .,13-(12) (Sine)
PU of Sine Sequence ctr #2 RO Control 237-l-(4)
PU of Multiply #2 38-l,2,3-(12) (Sine)
PU of Read Control Seq-31-(4) and Clutch Magnet
Controls read-in to Sine Sequence ctr #2
Controls reset of Sine Sequence ctr #2
Hold
PU of Read Control Seq-31-(4) and Clutch Magnet
Controls RO of SIO 24th col
Controls prevention of PU of Intermediate Reset 52--l,2,3-(12)
(Sine)
Controls prevention of PU of Intermediate In 50-l,2,3-(12)
(Sine)
PU of Intenimediate In 50-l,2,3-(12) (Sine)
Controls Sequence ctr reset to 1 (Sine)
PU of SM-3 # 83-l,2-(12,4)
Controls read-in to Sine Sequence ctr #2
Hold of 6 ,y and 5 233,234,235-l-(6)
Hold for .785 236-1,2, 3-(12, 12,4)
Controls read-in of sign to PQ 47th col (Sine)
PU of ft , f and S 233,234,235-l-(6)
Hold
Control prevention of PU of MC-DR Reset 47-1, .., 13-0.2) (Sine)
PU of Intermediate In 50-1,2, 3-(12) (Sine)
PU of DD-PQ reset 58-l,..,8-(12) (Sine)
Controls Sequence ctr reset to 4 (Sine)
Hold of .785 236-l,2,3-(12,12,4)j MC-DR Reset Control #1
239-l-(4)j MC-DR Reset Control #2 238-l-(12) (Sine)
Controls read-in to Sine Sequence ctr #2
Hold of SM-2 82-l-(:L2)
Controls read-in to Sine Sequence ctr #1
Hold
Relay
83-l,2-(12,4) S
(continued)
84-l-(6) S
SM-4
85-l-(4) D
SM-5
86-1- (4) D
Add-22 Control
87-l-(4) S
Q-Shift Elusive One
Control
D-2
88-l-(4) S
Q-Shift Elusive One
D-2
89-l-(4) S
Intermediate 24th col
Read-Out Control
M-l
90-l-(4) D
C Value to Intermediate
Control
91-1,2,3-(12) S
MC-DR Entry Control
(1-2)
M-l
Row
21
21
13
15
15
19
18
Contact
83-1-10
83-1-11 NC
83-1-12
83-2-1
83-2-3
84-1-1 NC
84-1-2 NC
84-1-3
84-1-4
84-1-6
85-1-1
86-1-1,2 NC
86-1-4
87-1-1
87-1-4
88-1-1,2
89-1-1
89-1-2
90-1-1,2
90-1-4
91-1-1
91-1-2,.., 91-2-11
91-3-1
91-3-2
91-3-3
91-3-4
91-3-5
91-3-6
91-3-7
91-3-8
91-3-12
Cycle
D-4
D-2
D-2
D-2
M-2
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-l
Function
PU of Intermediate In 50-1,2, 3-(12) (Sine)
PU of B . T'and o 233,234,235-l-(6)
Hold
Hold of ft, Y and S 233,234,235-l-(6) j Sine RO Control
240-l-(4)
PU of SIO Reset 228-1,2, 3-(l2,12,4)
Controls Sequence ctr (Sine)
Controls prevention of PU of DD-PQ Reset 58-1,.., 8- (12) (Sine)
PU of 7T/2 279-l,2,3-(l2,12,4)
PU of SIO Invert 242-l-(l2)
Hold
#
PU of Log Sine P-Out 72-l,2,3-(12,12,4)
Controls addition from Log "N" Switches to Q-Shift ctr
Hold
PU of Q-Shift Elusive One 88-1- (4)
Hold
Control read-in of Elusive One to Q-Shift ctr
PU of Sine Control #1 70-l-(4)
Controls RO of Intermediate ctr 24th col
PU of Intermediate In 50-l,2,3-(l2) (Int)
Hold
Controls circuit to MC-DR col 1 2nd mldg
Control circuit to MC-DR col 2-23 3rd mldg
Controls circuit of 1 impulse to 3rd mldg cols 1-6
Controls circuit of 1 impulse to 3rd mldg cols 7-12
Controls circuit of 1 impulse to 3rd mldg cols 13-18
Controls circuit of 1 impulse to 3rd mldg cols 19-23
Controls circuit of 8 impulse to 3rd mldg cols 1-6
Controls circuit of 8 impulse to 3rd mldg cols 7-12
Controls circuit of 8 impulse to 3rd mldg cols 13-18
Controls circuit of 8 impulse to 3rd mldg cols 19-23
Hold
CJ1
Relay
92-l,2,3-(12) S
MC-DR Entry Control
(3-6)
M-l
93-l,2,3-(12) S
MC-DR Entry Control
(4-8)
M-2
94-l-(4) S
Intermediate Invert
Control
M-l
95-l-(6) S
Place Limitation (643)
96-l-(6) S
Place Limitation (6431)
97-l-(6) S
Place Limitation (6432)
98-l-(6) S
Place Limitation (64321)
99-l,2,3-(12,12,4) S
Special PQ-Out
M-ll (Low order RO)
Row
21
18
18
18
18
22
Contact
92-1-1
92-1-2,.., 92-2-12
92-3-1
92-3-2
92-3-3
92-3-4
92-3-5
92-3-6
92-3-7
92-3-8
92-3-12
93-1-1
93-1-2,.., 93-2-12
93-3-1
93-3-2
93-3-3
93-3-4
93-3-5
93-3-6
93-3-7
93-3-8
93-3-12
94-1-1,2
94-1-4
95-1-1
95-1-6
96-1-1
96-1-6
97-1-1
97-1-6
98-1-1
98-1-6
99-1-1,.., 99-2-11
99-2-12
99-3-1,2
99-3-/+
Cycle
M-3
M-3
M-3
M-3
M-3
15-3
M-3
M-3
M-3
M-3
M-l
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-3
M-l
M-l
M-l
M-12
M-ll
M-ll
Function
Controls circuit to MC-DR col 1 2nd mldg
Control circuit to MC-DR col 2-24 3rd mldg
Controls circuit of 1 impulse to 3rd mldg cols 1-6
Controls circuit of 1 impulse to 3rd mldg cols 7-12
Controls circuit of 1 impulse to 3rd mldg cols 13-18
Controls circuit of 1 impulse to 3rd mldg cols 19-24
Controls circuit of 8 impulse to 3rd mldg cols 1-6
Controls circuit of 8 impu3.se to 3rd mldg cols 7-12
Controls circuit of 8 impulse to 3rd mldg cols 13-18
Controls circuit of 8 impulse to 3rd mldg cols 19-24
Hold
Controls circuit to MC-DR col 1 2nd mldg
Control circuit to MC-DR col 2-24 3rd mldg
Controls circuit of 1 impulse to 3rd mldg cols 1-6
Controls circuit of 1 impulse to 3rd mldg cols 7-12
Controls circuit of 1 impulse to 3rd mldg cols 13-18
Controls circuit of 1 impulse to 3rd mldg cols 19-24
Controls circuit of 8 impulse to 3rd mldg cols 1-6
Controls circuit of 8 impulse to 3rd mldg cols 7-12
Controls circuit of 8 impulse to 3rd mldg cols 13-18
Controls circuit of 8 impulse to 3rd mldg cols 19-24
Hold
PU of Intermediate Invert HD-1-(12)
Hold
PU of ,I 9 M relay 9-l-(4)
Hold
PU of "9" relay 9-1- (4)
Hold
PU of "9" relay 9-l-(4)
Hold
PU of "9" relay 9-l-(4)
Hold
Control RO of PQ cols 1-23 to Buss cols 1-23
Controls reading 9 to Buss ool 24 if PQ<0
PU of DD-PQ Invert HD-3-(l2)5 HD-3-(4) wc
Hold
Ol
Relay
Row
Contact
Cycle
Function
100-l-(4) D
Special Sign
M-ll (Low order RO)
22
100-1-1,2
100-1-4
M-ll
M-ll
PU of DD-PQ Invert HD-3-(l2); HD-3-(4) wc
Hold
101-1,2-(12) S
Normalizing Register
Read-In
22
101-1-1, ..,101-2-11
101-2-12
NR-2
NR-2
PU of Digit Sensing 102-1, ..,23-(4)
Hold
Norm. Reg. -2
102-1,.., 23-(4) D
22
1 < n ^ 23
Digit Sensing
Norm. Reg. -3
102-n-l
102-n-4
NR-3
NR-3
PU of Shift Positioning 103-1, ..,23-(4)
Hold
103-1,.., 23-(4) S
22
^ n ^ 22
Shift Positioning
Norm. Reg. -3
103-(n + 1)-1
103-(n -1- l)-2,3
103-(n + l)-4
NR-3
NR-4
NR-3
Controls reading of 1 to column (n 4- 1) of Intermediate ctr
Controls reading amount of shift n to cols 20 and 21 of Buss
Hold
104-1- (4) S
Normalizing Register RO
Norm. Reg. -4
22
104-1-1,2
104-1-4
NR-4
NR-4
Controls reading of amount of shift to cols 20 and 21 of Buss
Hold
HEAVY DUTY RELAYS
HD-1-(12)
Intermediate Invert
HD-1-1,..,10
HD-1-12
M-2
M-l
Control inverted RO of Intermediate ctr
Hold
M-l
HD-2-(12)
MC-DR Invert
HD-2-l,..,10
HD-2-11
D-7
D-ll
Control inverted RO of MC-DR ctrs
PU of F 18-l-(4)
D-6
HD-2-12
D-6
Hold
HD-3-(12)
HD-3-l,..,10
M-ll
Control inverted RO of DD-PQ ctrs
HD-3-(4) wc
DD-PQ Invert
HD-3-11
HD-3-12
D-15
M-ll
Controls RO of 9 from PQ 47th col if PQ <
Hold
M-ll
HD-3-1 wc
M-12
Controls RO of 9 from PQ 47th col if PQ ^
1-23 of PQ)
(Special RO c
HD-4-(12)
Intermediate Reset
HD-4-l,..,9
M-3
Control reset of Intermediate ctr
M-2
HD-5-(12)
MC-DR Reset
HD-5-l,..,9
M-10
Control reset of MC-DR ctrs
M-9
Relay
Row
Contact
Cycle
Function
HD-6-(12)
DD-PQ Reset
M-0
HD-6-l,..,9
M-l
Control reset of DD, PQ and Q-Shift ctrs
SEQUENCE RELAYS
S«q-8-(4)
Check Control
Seq-8-1,2
Seq-8-3
PU of Check relay-(4)
Hold
Soq-10-(4)
Storage RO Minus
Seq-10-1
Seq-10-4
PU of Invert relay-(12) for minus absolute RO
Hold
Seq-ll-U)
Storage RO Plus
Seq-11-1
Seq-11-4
PU of Invert relay-(12) for plus absolute RO
Hold
Seq-27-(4)
Repeat
Seq-27-1
Seq-27-2
Seq-27-4
PU of Start Seq-33-(4)j Hold of Start Interlock Seq-28-
PU of Start Seq-33-(4)
Hold
-(4)
Seq-28-(4)
Start Interlock
Seq-28-1 NC
Seq-28-4
PU of Start Seq-33-(4)
Hold
Seq-29-(12)
IVS Invert
Seq-29-l,..,9
Seq-29-12
Control 9's complement for inverted IVS RO
Hold
Seq-30-l,2,3~(12,12»4)
IVS Out
Seq-30-l-l,..,12
Seq-30-2-l,..,12
Seq-30-3-4
Control RO of IVS cols 1-12
Control RO of IVS cols 13-24
Hold
Seq-31-(4)
Read Control
Seq-31-1,2,3,4
Control reading of control tape through reading pins
Seq-32-(4)
Stop Control
Seq-32-1,2 NC
Seq-32-4
PU of Read Control Seq-31-(4) and Clutch Magnet
Hold
Saq-33-(4)
Start
Seq-33-1
Seq-33-3
Seq-33-4
PU of Read Control Seq-31-(4) and Clutch Magnet
PU of Start Interlock Seq-28-(4)
Hold
SWITCH RELAYS
SwA-l,2,3-(l2,12,4)
Switch A Out
SwA-l-l,..,12
SwA-2-l,..,12
SwA-3-4
Control RO of Switch A cols 1-12
Control RO of Switch A cols 13-24
Hold
Relay-
Row
Contact
Cycle
Function
Switch Invert-(12)
Sw Invert-1, ..,9
Sw Invert-11
Controls 9's complement for inverted RO
Hold
STORAGE COUNTER RELAYS
SCA-1,2,3-(12,12,4)
Storage Counter Out
SCA-4,5,6-(12,l2,4)
Storage Counter In
SCA-7,8-(12)
Storage Counter Carry
SCA-9-C4)
Storage Counter Carry
Control
SCA-10-(4)
Storage Counter 24th Col
Carry (10)
SCA-ll-(4)
Storage Counter 24th Col
Carry (9)
SCA-12,13-(4)
Storage Counter Carry
Booster
Storage Counter Invert-(12)
Storage Counter Reset-(12)
Sp64-(4)
Special 64 In
SCA-1-1,..,12
SCA-2-l,..,12
SCA-3-1
SCA-3-2
SCA-3-3
SCA-3-4
SCA-4-l,..,12
SCA-5-l,..,12
SCA-6-1
SCA-6-2
SCA-6-4
SCA-7-l,..,12
SCA-8-l,..,12
SCA-9-1
SCA-9-2
SCA-9-4
SCA-10-1
SCA-11-1
SCA-11-2
SCA-12-2,3
SCA-13-2,3
Invert-1,. .,9
Invert-10 NC
Invert-12
Reset-1,.,,9
Reset-10
Reset-11 NC
Reset-12
Sp64-1
Sp64-3
Sp64-4
Control RO of cols 1-12
Control RO of cols 13-24
PU of Str Ctr 24th Col Carry (relays 10 and 11)
PU of Str Ctr Reset relay-(12)
PU of Str Ctr Invert relay-(12)
Hold
Control read-in of cols 1-12
Control read-in of cols 13-24
PU of Str Ctr Carry Control SCA-9-(4)
PU of Str Ctr Reset-(12)
Hold
Control Carry for cols 1-12
Control Carry for cols 13-24
PU of Str Ctr Carry (relays 7 and 8)
PU of Str Ctr 24th Col Carry (relays 10 and 11)
Hold
Controls end around carry through 10
Controls end around carry through 9
PU of Str Ctr Invert relay-(12)
Control carry booster to col 1
Control carry booster to col 13
Control 9's complement for inverted RO
NC and Transfer paralleled to "9" spot
Hold
Control 10' s complement for reset of str ctr
Controls prevention of carry impulse during reset
NC and Transfer paralleled to "9" spot
Hold
HoldjPU of Normal Str Ctr In SC64-4,5,6-(l2,12,4)
PU of Carry Interlock-l-(6)
Hold
Relay
Sp65-(4)
Special 65 In
Sp68-(4)
Special 68 In
Sp69-(4)
Special 69 In
Carry Interlock-l-(6)
Carry Interlock-2-(6)
Choice-(6)
SC71-H-(6)
Normal Out Control
SC71-15-(6)
Special Out (direct)
SC71-l6-(6)
Normal In Control
SC71-17-(6)
Special In (direct)
Row
Contact
Sp65-1
Sp65-3
Sp65-4
Sp68-1
S P 68-3
Sp68-4
Sp69-1
Sp69-3
Sp69-4
CI-1-1,3
CI-1-3
C 1-1-4
C 1-1-5
C 1-1-6
CI-2-1,2
CI-2-3
C 1-2-4
C 1-2-5
C 1-2-6
Choice-1
Choice-2
Choice-6
SC71-14-1
SC71-14-2
SC71-14-3
SC71-14-6
SC71-15-1
SC71-15-2
SC71-15-6
SC71-16-1
SC71-16-2
SC71-16--3
SC71-16-6
SC71-17-1
SC71-17-2
SC71-17-3
SC71-17-6
Cycle
Function
Hold; PU of Normal Str Ctr In SC65-4,5,6-(12,12,4)
PU of Carry Interlock-l-(6)
Hold
Hold; PU of Normal Str Ctr In SC68-4,5,6-(12,12,4)
PU of Carry Interlock-2-(6)
Hold
Hold; PU of Normal Str Ctr In SC69-4,5,6-(12,12,4)
PU of Carry Interlock-2-(6)
Hold
Control end around carry from col 24 of ctr 65 to col 1 ctr 64
Controls carry from col 23 of ctr 65 to col 24 of ctr 64
Controls carry from col 23 of ctr 64 to col 1 of ctr 65
PU of Carry Control SC64-9-(4) or SC65-9-(4) '
Hold
Control end around carry from col 24 of ctr 69 to col 1 ctr 68
Controls carry from col 23 of ctr 69 to col 24 of ctr 68
Controls carry from col 23 of ctr 68 to col 1 of ctr 69
PU of Carry Control SC68-9-(4) or SC69-9-(4)
Hold
PU of 24th Col 9 SC70-ll-(4)
PU of Str Ctr Invert- (12)
Hold; PU of 24th Col 9 SC70-ll-(4)
PU of Normal Str Ctr Out SC71-1-(12)
PU of Normal Str Ctr Cut SC71-2-(l2)
PU of Normal Str Ctr Out SC71-3-(4)
Hold
PU of Normal Str Ctr Out SC71-2-(12)
PU of Normal Str Ctr Out SC71-3-(4)
Hold
PU of Normal Str Ctr In SC71-4-(12)
PU of Normal Str Ctr In SC71-5-(l2)
PU of Normal Str Ctr In SC71-6-(4)
Hold
PU of Normal Str Ctr In SC71-5-(12)
PU of Normal Str Ctr In SC71-6-(4)
PU of Carry Back Control SC71-20-(6)
Hold
en
>*»
oo
Relay
SC71-18-1,2-(12,6)
Special Out (shifted)
SC71-19-1,2-(12,6)
Special In (shifted)
SC71-20-(6)
Carry Back Control
Check-(4)
Row
Contact
SC71-16-1-1,..,12
SC71-18-2-1
SC71-18-2-6
SC71-19-1-1,..,12
SC71-19-2-1
SC71-19-2-2
SC71-19-2-6
SC71-20-1
SC71-20-1 NC
SC71-20-6
Check-1
Check-4
Cycle
^ Function
Control RO of ctr 71 cols 13-24 to Buss cols 1-12
PU of Normal Str Ctr Out SC71-3-(4)
Hold
Control read-in to ctr 71 cols 13-24 from Buss cols 1-12
PU of Normal Str Ctr In SC71-6-(4)
PU of Carry Back Control SC71-20-(6)
Hold
Controls carry back in ctr 71 from col 24 to col 13
Controls carry back in ctr 71 from col 24 to col 1
Hold
PU of Read Control Seq-31-(4) and Clutch Magnet
Hold
en
tfc.
CD
CM CONTACTS
i
Cam
Make
Break
Function
Cam
Make
Break
Function
CC-1
1/16 1
1 5/8
1 impulse control
CC-25
3
14
Hold of PQ 23rd Column 68-l-(4)
CC-2
1/16 2
2 5/8
2 impulse control
CC-26
2
1 1/3
PU of MP-DIV Control Pick-Up
13-l-(6)
CC-3
1/16 3
3 5/8
3 impulse control
CD Control 69-1, 2-(4)
CC-4
1/16 4
4 5/8
4 impulse control
CC-27
9
12
Hold of DR Compare 2-1, . . ,120-(4)
CC-5
1/16 5
5 5/8
5 impulse control
CC-28
9
12
Hold of DD Compare 6-1,. .,,24- (12)
DR Compare 2-121, . . ,2l6-(4)
CC-6
1/16 6
6 5/8
6 impulse control
CC-29
6
8
Hold of A 12-1, 2-(4)
CC-7
1/16 7
7 5/8
7 impulse control
PU of Sign Control #2 71-l-(4)
B l6-l-(4)
CC-30
1/16 3
1
Hold of C 2 66-l-(4)
CC-8
1/16 8
8 5/8
8 impulse control
(69-1-3 NC)
D 2 67-l-(4)
CC-9
1/16 9
9 5/8
9 impulse control
PU of Sign Control #1 7C~1»(4)
CC-31
12 1/2
9
PU of Times Right
5-l,..,27-(12,12,4)
F 18-1-(4J
G 19-l-(4)
CC-1 ,,..,9
PU of DD Compare 6-1, ..,24-(l2)
DR Compare 2-1,.., 216-00
CC-32
8 31/2
2
Hold of MP-DIV Control Hold
CC-10
1/2
Controls impulse to Seq Ctr Magnet
(12-1,2-2 NC)
14-1-(12)
F 18-l-(4)
CC-12
12
12 1/2
Controls carry impulse
G 19-l-(4)
CC-15
15
15 1/2
15 impulse control
CC-33
14
15 1/3
PU of Shift 36-l,..,39-(4,6 or 12)
C 30-l-(12)
D 31-1-(12)
CC-16
16
16 1/2
16 impulse control
Q-Shift 33-1,.., 80- (4, 6 or 12)
CC-17
L
L 5/8
CB make 16 points
H 20-l-(4)
DD-PQ Invert HD-3-(12)j
CC-19
L
L 5/8
CB :oaake 16 points
HD-3-(4) wc
CC-21
1/16 L
L 1/2
CB break 16 points
CC-34
9
12
Hold of Over Under 1-1, . „,235-(4)
CC-23
1/16 L
L 1/2
CB break 16 points
CC-35
9
12
Hold of Over Under 1-236, . ,,423-(4)
Digit Sensing 102-1,.. ,23-00
CC-24A
L 1/4
L 7/8
Compare control make
CC-36
12
Hold of Column Shift Right
CC-24B
L 1/4
L 7/8
Compare control make
29-l,..,36-(12,12,6)
Column Shift Left
CC-24C
L 1/16
L 3/4
Compare control break
21-1,..,36-(12,12,6)
Times Right 5-1,.., 27- (12, 12, 4)
CC-24D
L 1/16
L 3/4
Compare control break
Times Left 4-l,..,27-(12,12,4)
E 17-l-(4)
CAM CONTACTS
Cam
Make
Break
Function
Cam
Make
Break
Function
CC-37
CC-38
CC-39
CC-40
11
11 1/2
1/3 15
1/16 15
lA 12
12
CC-41
(30-1-1,2 NC)
(30-1-8,9 NC)
(31-1-1,2 NC)
(31-1-8,9 NC)
CC-42
CC-43
12
12
12
15
1/3 16
PU of Q-Control 7-l,..,9~(4)
No Go 63-l-(4)
Shift Positioning
103-1,.., 23-(4)
Hold of C 30-1- (12)
D 31-1-(12)
Q-Control 7-1,.., 9- (4)
No Go 63-l-(4)
Hold of Compare In 3-1,. .,24-(l2);
3-25-(4)
MC-DR Invert HD-2-(l2)
PU of DD-PQ Transfer #1
74-l,2,3-(l2,12,4)
DD-PQ Transfer #2
59-l,2,3-(12,12,6)
MP Reset 40-1,2, 3-(12)
MC-DR Reset 47-l,..,13-(12)
DD-PQ Invert HD-3-(12)j
HD-3-(4) wc
Compare In 3-1, ..,24-(12) ;
3-25-(4)
MC-DR Invert HD-2-(12)
Log Sine P-Out
72-l,2,3-(l2,12,4)
Special Sign 100-l-(4)
Hold of MP Cycle Control
37-l,..,26-(4,6 or 12)
Hold of Shift Pick-Up
35-l,..,46-(4)
Hold of Intermediate In
50-l,2,3-(12)
DD-PQ Reset 58-1, . .,8-(12)
Intermediate Invert Control
94-l-(4)
Intermediate Invert HD-1-(12)
MC-DR In 43-l,..,10-(12)j
43-H,12-(4)
CC-43
(continued)
CC-44
1 1/3
CC-45
1/16 11
13
Shift 36-l,..,39-(4,6 or 12)
Intermediate Reset
52-l,2,3-(l2)
Intermediate Reset KD-4-(l2)
First Build Up
44-l,..,5-(12)
First and Second Build Up
45-l,..,5-(12)
Second Build Up 46-l,..,5-(12)
MP In 39-l,2,3-(12)
DD-PQ Transfer #1
74-l,2,3-(l2,12,4)
DD-PQ Transfer #2
59-l,2,3-(12,12,6)
MP Reset 40-l,2,3-(12)
MC-DR Reset 47-1,. .,13-(12)
P-Out 34-l,2,3-(12); 34-4-(4)
Sequence Counter Reset
48-l-(12)
DD-PQ Invert HD-3-(12)j
HD-3-(4) wc
Q-Shift Invert 22-l-(12)
Add-22 32-l-(4)
DD In 57-l,2,3-(l2)
Q-Shift 33-l,..,80-(4,6 or 12)
H 20-1- (4)
Normalizing Register Read- In
101-1,2-(12)
Normalizing Register Read-Out
104-l-(4)
PU of Intermediate Carry Control
23-l-(4)
MC-DR Carry Control 26-l-(4)
PQ Carry Control 24-l-(4)
DD Carry Control 27-l-(4)
Q-Shift Elusive One Control
87-1-U)
Q-Shift Carry Control 25-l-(4)
Elusive One 60-l,..,23-(4)
F Control 64-l-(4) '
G Control 65-l-(4)
"9" 9-l-(4)
PU of Intermediate Carry
53-l,2-(12)
CAM
CONTACTS
Cam
Make
Break
Function
Cam
Make
Break
Function
CC-45
MC-DR Carry 49-1,.. ,10-(12)
PQ Carry 62-l,..,4-(12)
CC-53
11
16
Hold of Divide 56-l,..,13-(12)
(continued)
(199-1-1 NC)
DD Carry 61-1,..,4-(12)
Q-Shift Elusive One 88-l-(4)
CC-54
12
12 1/2
Controls impulse to cycle ctr
Q-Shift Carry 28-l-(4)
magnet
CC-46
2
13 1/3
Hold of Intermediate Carry Control
23-l-(4)
MC-DR Carry Control 26-l-(4)
PQ Carry Control 24-l-(4)
DD Carry Control 27-l-(4)
Q-Shift Elusive One Control
87-l-(4)
Q-Shift Carry Control 25-l-(4)
CC-55
12 1/2
13 2/3
Controls Sequence ctr RO-B
PU of Intermediate In
50-l,2,3-(12)
First Build Up 44-1, ..,5- (12)
MP-In 39-l,2,3-(12)
Sequence ctr Reset 48-1- (12)
Shift Pick-Up 35-1,.., 46-(4)
Elusive One 60-l,..,23-(4)
CC-56
12 1/2
13 2/3
Controls Sequence ctr RO-C
F Control 64-l-(4)
G Control 65-l-(4)
PU of MC-DR In 43-1,. .,10-(12)j
43-ll,12-(4)
First and Second Build Up
CC-47
3 1/2
16
Hold of MP-DIV Control Pick-Up
13-l-(6)
CD Control 69-1, 2-(4)
Special Sign 100-l-(4)
45-l,..,5-(12)
MC-DR Reset 47-1,.., 13- (12)
Q-Shift Invert 22-1- (12)
DD-In 57-l,2,3-(12)
CC-48
2
4
Hold of "9" 9-l-(4)
CC-57
12 1/2
13 2/3
Controls Sequence ctr RO-D
PU of DD-PQ Reset 58-l,,..,8-(l2)
CC-49
1
1/3
PU of Multiply #2 38-l,2,3-(l2)
Intermediate Invert Control
94-l-(4)
CC-50
1/3 3
16
Hold of XG 15-l-(4)
Intermediate Reset
(55-2-6 NC)
EX-1 54-l-(12)
52-l,2,3-(12)
Second Build Up 46-l,,..,5-(12)
CC-51
2
1 1/3
PU of LE 10-1- (4)
LF ll-l»2-(6,4)
XG 15-l-(4)
P-Out 34-l,2,3-(12)j 34-4-(4)
Add-22 32-l-(4)
EX-2 55-l,2,3-(12,12,6)
CC-58
14
15 1/3
PU of MP-DIV Control Hold 14-1-(12)
Column Shift Right
CC-52
1/3 3
16
Hold of Multiply #1 41-1,2-(12)
29-l,..,36-(12,12 ;( 6)
(4S-1-1 NC)
Multiply #2 38-l,2,3-(12)
Divide 56-1,.., 13- (12)
E 17-l-(4)
D 2 67-l-(4)
LE 10-l-(4)
LF ll-l»2-(6,4)
M 42-l,2,3-(12,12,4)
CC-59
14
15 1/3
PU of Column Shift Left
21-1,..,36-(12,12 1 ,6)
C 2 66-1-U5
EX-2 55-1, 2,3-(12, 12,6)
IM-1 78»1,2,3-(12.12,4)
IM-2 79-l,2-(12,4)
CC-60
6
5 1/3
PU of A 12-1, 2-(4)
SM-1 8L-1,2,3-(12,12,4)
B 16-1-U5
G 19-l-(4)
SIJ5-5 85»l-(4)
Shift Positioning 103-1,.., 23-(4)
CM CONTACTS
Cam
CC-61
CC-62
CC-63
CC-64
CC-65
CC-66
CC-67
CC-68
CC-69
CC-70
Make
CC-71
CC-72
CC-73
CC-74
(47-13-1 NC
CC-75
(52-3-6 NC)
12
14
12
4
12
2
15 3/4
2
1 1/3
15
16 1/3
14
15 1/3
15
16 1/3
14
1/2
14
13 1/2
11
Break
16
15 1/3
2
15 1/3
16
Function
PU of Intermediate Reset HD-4-(12)
PU of DD-PQ Reset HD-6-(12)
PU of MC-DR Reset HD-5-(12)
PU of EIO Reset 218-1,2,3-(12)
PU and hold of SM-4 84-l-(6)
PU and hold of SM-3 83-l,2-(12,4)
PU of C6-0 Step Control 223-1-U)
PU of log C values
210-1,.., 6-(24,28)
PU of SIO Out #2 Control 237-l-(4)
SIO Reset 228-1, 2, 3- (12)
PU of Intermediate Invert HD-1-(12)
1/211 etc
243-1,.., 21-(4,6 or 12)
Hold of .785 relay
236-l,2,3-(12,6,4)
MC-DR Reset Control #1
239-1- (4)
MC-DR Reset Control #2
238-l-(12)
PU of V/2 279-l,2,3-(12,12,4)
r 278-l,2,3-(12,12,4)
2 r280-l,2,3-(12,12-4)
SIO Invert 242-l-(12)
Hold of SM-3 83-l,2-(12,4)
PU of LM 42-l,2,3-(12,12,4)
SIO Out #3 272-l,2,3-(12,12,4)
Hold of Sign Control #2 71-l-(4)
Hold of Sign Control #1 70-l-(4)
Cam
CC-76
CC-77
CC-78
CC-79
CC-80
Make
15
Break
16 1/3
16
15
6
1/16 12
16
5 1/3
9
Function
PU of MC-DR Entry Control (1-2)
91-1,2,3-(12)
MC-DR Entry Control (3-6)
92-l,2,3-(12)
MC-DR Entry Control (4-8)
93-l,2,3-(12)
EIO In 217-1, 2,3-(12, 12,4)
EIO 1-18 Out 219-1, 2-(12)
Hold of MC-DR Entry Control (1-2)
91-1 2 3-(l2)
MC-DR Entry Control (3-6)
92-l,2,3-(12)
MC-DR Entry Control (4-8)
93-l,2,3-(l2)
PU of Times Right
5-l,..,27-(l2,12,4)
Times Left
4-l,..,27-(l2,12,4)
PU of F 18-l-(4)
Controls impulse to Cycle ctr magnet
PU of Compare Control 8-l-(4)
STORAGE CAMS
Cam
SC-1
SC-2
SC-3
SC-4
SC-5
SC-6
SC-7
SC-8
SC--9
SC-10
SC--11
Make
1
2
3
4
5
6
7
6
9
12
12
Break
1 1/2
2 1/2
3 1/2
4 1/2
5 1/2
6 1/2
7 1/2
8 1/2
9 1/2
12 1/2
Function
1 impulse control
2 impulse control
3 ^impulse control
4 impulse control
5 Impulse control
6 JLmpulse control
7 JLmpulse control
8 .impulse control
9 :Lmpulse control
Control carry impulse
Hold of
Str Ctr In SCA-1,2,3-(12,12,4)
Str Ctr Out SCA-4,5,6~(12,12,4)
Check Relay- (4)
Invert Relay-(12)
Reset Relay-(12)
High Accuracy Ctrs Special In
Sp64-l-(4) etc.
Ctr 71 Normal Out Control
SC71-14-(6)
Ctr 71 Normal In Control
SC71-l6-(6)
Ctr 71 Special Out (direct)
SC71-15-(6)
Ctr 71 Special Out (shifted)
SC71-18-1,2-(12,6)
Ctr 71 Special In (direct)
SC71-17-(6)
Ctr 71 Special In (shifted)
SC7X-19-1,2-(12,6)
Switch Out SwA-l,2,3-(12,l 2 >4)
Switch Invert Relay- (12)
PU of Ctr 71 Normal Out
SC71-1,2,3-(12,12,6)
Ctr 71 Normal In
SC71-4,5,6-(12,12,6)
Cam
SC-12
SC-13
SC-14
SC-15
SC-16
SC-17
SC--18
Make
11
13
14
14
14
Break
14
1 1/2
14 1/16
15 1/3
15 1/3
14 1/2
H 1/2
Function
PU of Carry SCA-7,8-(12)
24th Column Carry SCA-10,ll-(4)
Check Relay-(4)
PU of Carry Control SCA.-9-(4)
High Accuracy Carry Interlock
CI-l,2-(6)
Ctr 71 Carry Back Control
SC71-20-(6)
Hold of Carry Control SCA-9-(4)
High Accuracy Carry Interlock
CI-l,2-(6)
Ctr 71 Carry Back Control
SC71-20-(6)
PU of 24th Column Carry
SCA-10,11"(4)
Hold of Choice Relay-(6)
PU of Reset Relay-(12)
Invert Relay-(12) to be used
with Choice Counter
PU of Invert Relay-(12) for minus
absolute value RO
PU of Invert Relay-(12) for plus
absolute value RO
MP-DIV RELAYS AND FUSES
Relay No.
1-row
1-row
1-row
1-row
1-row
1-row
1-row
1-row 8
1-row 9
2-row
2-row
2-row
2-row
2-row
2-row
2-row
2-row 8
2-row 9
3-1,.., 24
3-25
4
5
6
7
8
9
10
11
12-1
12-2
13
14
15
16
17
18
19
20
21
22
23
24
Fuse No.
23
24
25
26
27
28
29
30
31
14
15
16
17
18
19
20
21
22
33
38
32
32
34
34
34
34
34
34
34
35
34
34
34
34
34
34
34
34
35
35
35
35
Relay No.
25
26
27
28
29
30
31
32
33
34-1,2,3
34-4
35
36
37
38
39
40
41
42
43-1,.., 10
43-11
43-12
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
Euse No.
35
35
35
35
35
35
35
35
38
39
40
40
41
36
37
37
37
37
37
42
36
41
42
42
42
42
42
43
43
43
43
43
43
43
44
39
39
39
45
45
45
34
Relay No.
Fuse No.
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
99A
Shift Circuit
Low Order P-Out
Heavy Duty
35
35
38
38
38
40
39
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
36
41
41
39
43
32
32
32
38
43
43
43
43
47
47
47
47
46
en
MP-DIV RELAYS AND FUSES
en
en
Fuse No,
Relay No.
1 Intermediate Counter Magnets
2 MC-DR Counter Magnets (1-2)
3 MC-DR Counter Itegnets (3-6)
4 MC-DR Counter )£agnets (4-6)
5 MC-DR Counter Magnets (5)
6 MC-DR Counter Magnets (7)
7 MC-DR Counter Magnets (9)
8 MP Counter Magnets
9 DD Counter Magnets columns} 1-24
10 DD Counter Magnets columns! 25-45
11 PQ Counter Magnets: columns 1-24
12 PQ Counter Magnets: columns 25-46 and 47
13 Q-Shift, Sequence, and Cycle Counter Magnets
14 2- 1st row
15 2- 2nd row
16 2- 3rd row
17 2- 4th row
18 2- 5th row
19 2- 6th row
20 2- 7th row
21 2- 8th row
22 2- 9th row
23 1- 1st row
24 1- 2nd row
Fuse No.
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
Relay No,
1- 3rd row
1- 4th row
1- 5th i'ow
1- 6th row
1- 7th row
1- 8th row
1- 9th row
4,5,91,92,93
fn "i 24)
6,7,8;9*10,11,(X2-1), 13,14,15,16,17,18,19,20,63
(12-25,21,22,23,24,25,26,27,28,29,30,31,32,64,65
37,(43-11)
(3-255/33!6ot67,68,71,72,73,74,75,76,77,78,79,80,
81,82,83,84,85,86,94
(34-1,2,3), 57, 58, 59,70,89
(34-4) ,35,69
36^3-1487,88
(43-1, .. ,10) ,44,45,46,47,48
49,50,51,52,53,54,55,90,95,96,97,98
56
60,61,62
Heavy Duty Relays
99, 99A, Shift Circuit, Low Order P-Out
557
INDEX
The references are to pages.
Abacus, 1.
Abbreviations, used in appendices, 405.
used in bibliography, 397.
Absolute value, 16.
check counter, 20, 131.
choice counter, 17.
coding, 110.
operation, 65.
Accuracy, 51.
in division, 26, 120, 249.
in high accuracy computation, 23, 151.
in subtabulation, 225.
of exponential unit, 32, 165.
of functional tapes, 196.
of logarithm unit, 30, 162.
of sine unit, 33, 182.
Addition, 3, 14, 60.
coding, 107, 109.
Aiken, H. H., 27, 52.
Algebraic sign, 3, 12, 78.
choice counter, 17, 129.
in high accuracy computation, 142.
of arguments in functional tapes, 195.
Analytical engine, 5.
Argument control, 236.
coding, 238.
plugging, 276.
Asymptotic expansions, 369.
Automatic check counter, see Check counter.
Automatic codes, 15, 99.
circuits, 433.
Babbage, Charles, 1, 4, 7.
analytical engine, 5.
difference engine, 4, 6.
Bessel functions, 335, 337.
Bibliography of numerical analysis, 338.
Build-up, 75.
Cam, 12, 53, 60.
list, 550.
Card feed, 42.
coding, 229.
operation, 96.
operating instructions, 290.
plugging, 272.
Card punch, 42, 44.
checking, 233.
coding, 231, 241.
operation, 93.
operating instructions, 290.
plugging, 274.
serial and code numbers, 134, 140, 229,
234,251.
timing, 106.
Cards, Hollerith, 5.
International Business Machines, 95.
Jacquard, 5.
serial and code numbers, 134, 140, 229,
234, 251.
Carry, 1, 2, 4.
circuit, 63.
contact, 61.
in ganged counters, 20, 143.
in MIO counter, 133.
in multiplicand-divisor counters, 69.
in SIO counter, 139.
in print counters, 95, 236.
in punch counter, 93, 231.
See also End around carry.
Cascade relays, 53, 93.
list, 411.
Central difference interpolation, 206.
Check counter, 20.
circuits, 455.
coding, 131, 241.
Checks, 131.
of functional tapes, 199.
of general computation, 287.
of printed data, 240.
of punched cards, 233.
operating instructions, 291.
Choice counter, 17.
circuits, 449.
coding, 108, 110, 129.
Code, 12, 98.
automatic, 15, 99.
non-automatic, 99, 101.
Code numbers, see Cards.
Coding, 12, 98.
Commutator, 59.
Compare cycle, 84.
Comparison, 25.
plugging, 249.
timing, 105.
See also Division and Place limitation.
Complements on nine and ten, 2.
in division, 25.
558
INDEX
in resets, 16.
in read-outs, 82,
in subtraction, 14.
Control tapes, see Sequence control tapes.
Cosine, 183.
Counter, see Check counter,
Choice counter,
Cycle counter,
Dividend counter,
Doubling counter,
Exponential in-out counter,
Functional counter,
Ganged counters,
Interpolation counters,
T.rvrQTMtVim /»r»«*>^*>'»*
Logarithm in-out counter,
Multiple in-out counter,
Multiplicand-divisor counter,
Multiplier counter,
Print counter,
Product-quotient counter,
Punch counter,
Quotient-shift counter,
Sequence counter,
Sign counter,
Sine in-out counter,
Storage counter.
Counter wheel, 2.
See also Storage counter.
Cycle, 15, 51, 60, 105.
C^cle counter- 74*
Determinants, bibliography, 341.
Difference engine, 4, 6.
Difference equations, bibliography, 362.
Differences, bibliography, 359.
central difference interpolation, 206.
evaluation of polynomial, 296, 300.
method of checking, 132.
methods of differencing, 202.
Newton-Gregory formula, 217.
subtabulation, 224.
TVIffa-»»or»+ial amj^tinrto nrrfimi
fw W i r»cri»a —
phy, 375.
partial, bibliography, 385.
Differentiation, numerical, bibliography, 371 ,
Discontinuous functions, 16, 129.
Dividend counter, 69.
Division, 24.
circuits, 499.
coding, 120.
in high accuracy computation, 151.
operation, cycle by cycle, 80.
place limitation, 26, 120, 249.
plugging, 249.
switch, 25, 120, 250.
timing, 105.
Doubling counter, 137, 140.
Doubling read-out, 68.
Electrical circuits, 53.
Elusive one, 25.
Emergency stop switch, 57.
End around carry, 3.
in check counter, 20, 131.
in division, 25, 72.
in ganged counters, 143.
in LIO counter, 137.
in MIO counter, 133.
in punch counter, 95.
in SIO counter, 36.
Exponential in-out counter, 31 .
coding, 99, 100, 101.
plugging, 256.
Exponential unit, 30.
coding, 165.
plugging, 256.
timing, 105.
False position, rule of, see Rule of false
position.
Feed, see Card feed.
Finite differences, see Differences.
Functional counter, 67, 90.
Functional tapes. 38 ; 45. 47. 185.
che eking, 199.
design, 195.
reading, 92.
Fuse, 555.
Ganged counters, 20.
coding, 142,
See also High accuracy computation.
Grant, G. B„ 6.
Half -correction, coded, 129.
Half pick-up, see Half-correction.
Hankel functions, 332, 337.
Harmonic analysis, bibliography, 356.
Heavy duty relays, 545.
High accuracy computation, 20, 23.
circuits, 446, 494.
coding, 142.
plugging, 247, 253.
Hollerith cards, 5.
Hyperbolic functions, 38, 167.
Implicit functions, bibliography, 355.
559
INDEX
Impulses, 59.
In relays (B relays), 12, 53.
list, 422.
Independent variable switch, 50.
coding, 107.
Integral equations, bibliography, 393.
Integral, evaluation of definite, bibliogra-
phy, 371.
example, 318.
Integration, numerical, bibliography, 371,
Intermediate counter, 68.
Interpolation, 10, 38.
bibliography, 363.
central difference, 206.
counters, 92.
inverse, 227.
Newton-Gregory formula, 217.
plugging, 262.
switches, 185, 193, 195, 271.
tables, bibliography, 368.
Taylor's series, 196.
timing, 105.
Interpolation counters, 38, 92.
Interpolators, 38.
coding, 185.
multiple use, 193.
plugging, 262.
switches, 185, 193, 195, 271.
Interposition, 22.
in division, 120.
in multiplication, 111.
in printing, 240.
in tape positioning, 187.
of machine stops, 241.
Inverse interpolation, 227.
bibliography, 368.
Invert codes, 107, 110.
Invert relay, 14, 62.
Iterative processes, 170.
bibliography, 348, 352.
coding, 170.
example, 304.
high accuracy division, 151.
in division, 27.
inverse interpolation, 227.
rule of false position, 179.
Newton Raphson formula, 170.
Jacquard cards, 5.
Keyboard, in testing, 289.
See also Tape punch.
Least squares, bibliography, 344.
Leibnitz, Gottfried, 3.
Linear algebraic equations, bibliography, 341.
example, 335.
Logarithm counter, 28.
Logarithm in-out counter, 28, 37.
coding, 137.
plugging, 251, 254.
Logarithm unit, 28.
coding, 162.
plugging, 254.
switch, 162, 255.
timing, 105.
Machine methods in arithmetic, bibliogra-
phy, 340.
Manual punch, 45.
Matrices, bibliography, 341.
Mechanical drive, 58.
Miscellaneous relays (C relays), 12, 53.
list, 429.
Molding, 59.
multiple molding counters, 67.
Morland, Samuel, 3.
Muller, J. H., 4.
Multiple in-out counter, 18.
coding, 133.
Multiplicand-divisor counters, 68.
Multiplication, 21.
circuits, 457.
coding, 111.
in high accuracy computation, 145.
operation, cycle by cycle, 74.
plugging, 247.
timing, 105.
Multiplier counter, 69.
Multiply-divide relay list, 528.
Napier, John, 1 .
Newton-Bessel central difference formula, 206.
Newton-Gregory interpolation formula, 217.
Newton Raphson formula, 27, 170.
Newton-Stirling central difference formula, 206,
No-go, 26, 84.
Non-automatic codes, 99, 101.
Normalizing register, 24.
circuits, 495.
coding, 159.
Numerical analysis, bibliography, 338.
Odd functions, 17, 129.
Operating decimal position, 21.
See also Plugging.
Operating instructions, 50, 289.
examples, 295, 299, 302, 312, 315, 326.
Out relays (A relays), 11, 53.
list, 411.
560
INDEX
Pascal, Blaise, 2.
Periodogram analysis, bibliography, 357.
Place limitation, 26, 120, 249.
Plugboard, 21, 272, 274.
Plugging, 21, 50, 245.
Plugging instructions, 291.
examples, 296, 300, 303, 313, 316, 329.
Polynomial, evaluation, 292, 296, 300.
Print counter, 43, 95.
Printing, 43.
argument control, 236, 238, 276.
coding, 236.
half pick-up, 236, 238, 278.
operation, 95.
operating instructions, 290.
plugging, 275.
timing, 106.
Product-quotient counter, 21, 72.
I-.-, nw foi- -.««,?_«„* 9
iuw uiuci i cau-uuij a<j>, i-xu, ioa,
Punch, see Card punch and Manual punch.
Punch counter, 43, 93.
See also Card punch.
Quotient shift counter, 25, 72.
Read-in, 59.
Reading pins, 11, 53.
Read-out, 62.
Reciprocals, 175.
Newton Raphson rule, 27.
Registers, circuits, 437.
constant, see Switches.
storage, see Storage Counters.
Relay, 12, 53.
list, 528.
table 91.
Rerun instructions, 50, 291.
Reset, 16, 64.
coding, 110.
manual, 50, 291.
Roots, bibliography, 345.
cube, 172,
square. 170.
Rule of false position, 179.
bibliography, 348.
Scheutz, George, 6.
Sequence control mechanism, 11, 50, 53.
subsidiary sequence controls, 22, 50, 57,
73, 91.
Sequence control tape, 11, 45, 48, 53.
checking, 289.
examples, 294, 298, 301, 307, 314, 322.
332, 335.
Sequence counter, 73.
Sequence relays, 53.
list, 546.
Serial numbers, see Cards.
Shift counters, 37.
See also Logarithm in-out counter,
Multiple in-out counter,
Normalizing register,
Sine in-out counter.
Sign counter, 72.
Sine in-out counter, 34, 37.
coding, 139.
plugging, 252, 258.
Sine unit, 33.
coding, 182.
plugging, 258.
switches, 139.
timing, 105.
Slide rule, 2.
ujjuU) v,uuiiuuwvui , war.
Start, circuits, 53, 431.
key, 50.
Starting tapes, 290.
examples, 293,297,300,305,314,318,335.
Stop, circuits, 53, 431.
key, 50.
Storage counters, 14, 59.
coding, 109.
relays, 547.
Subtabulation, 224.
bibliography, 368.
Subtraction, 2, 14.
coding, 107, 109.
Switches, 12.
coding, 107.
independent variable switch, 50.
relays, 546.
Table relays, 29, 34, 91.
plugging, 258.
Tabulating machine cards, see Card feed, Card
punch and Cards.
Tape library, 50, 292, 335, 336.
Tape punch, 45.
Tapes, functional, 38, 45, 47, 185.
sequence control, 11, 45, 48, 53.
value, 41, 45, 46, 185.
Taylor's series, 196.
Timing, 50, 105.
of typical problems, 296, 300, 303, 313,
316, 317, 329, 336.
Tolerance, 20, 131.
Transcendental functions, 27, 38.
Typewriters, see Printing*
Value tape, 41, 45, 46, 185.
561
INDEX
coding, 189.
reading, 92.
Zero, of a polynomial, bibliography, 345, 348.
of transcendental equations, bibliogra-
phy, 352.
positive and negative, 3, 129.
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